Relevant bibliographies by topics / Hamiltonian Boundary Value Method

Academic literature on the topic 'Hamiltonian Boundary Value Method'

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Published: 10 March 2023

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Journal articles on the topic "Hamiltonian Boundary Value Method"

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Song, Mingzhan, Xu Qian, Hong Zhang, and Songhe Song. "Hamiltonian Boundary Value Method for the Nonlinear Schrödinger Equation and the Korteweg-de Vries Equation." Advances in Applied Mathematics and Mechanics 9, no. 4 (January 18, 2017): 868–86. http://dx.doi.org/10.4208/aamm.2015.m1356.

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AbstractIn this paper, we introduce the Hamiltonian boundary value method (HBVM) to solve nonlinear Hamiltonian PDEs. We use the idea of Fourier pseudospectral method in spatial direction, which leads to the finite-dimensional Hamiltonian system. The HBVM, which can preserve the Hamiltonian effectively, is applied in time direction. Then the nonlinear Schrödinger (NLS) equation and the Korteweg-de Vries (KdV) equation are taken as examples to show the validity of the proposed method. Numerical results confirm that the proposed method can simulate the propagation and collision of different solitons well. Meanwhile the corresponding errors in Hamiltonian and other intrinsic invariants are presented to show the good preservation property of the proposed method during long-time numerical calculation.
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Brugnano, L., and D. Trigiante. "Block Boundary Value Methods for linear Hamiltonian systems." Applied Mathematics and Computation 81, no. 1 (January 1997): 49–68. http://dx.doi.org/10.1016/0096-3003(95)00308-8.

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Brugnano, Luigi, Gianluca Frasca Caccia, and Felice Iavernaro. "Efficient implementation of Gauss collocation and Hamiltonian boundary value methods." Numerical Algorithms 65, no. 3 (January 17, 2014): 633–50. http://dx.doi.org/10.1007/s11075-014-9825-0.

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Erbe, L. H., Xinzhi Liu, and Jianhong Wu. "Solvability of boundary value problems for vector differential systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 114, no. 3-4 (1990): 181–93. http://dx.doi.org/10.1017/s0308210500024379.

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SynopsisBrouwer topological degree theory, the shooting type method, the disconjugacy theory of Hamiltonian systems and the Liapunov-Razumikhin technique of Volterra integrodifferential equations are employed to establish some solvability results for the 2n-dimensional differential systemsubject to one of the following boundary conditions:(i) x(0) = Qx(l), Qg(l x(1), qy(1)= g(0, x(0), y(0)),(ii) Blx(O) = B2g(O, x(O), y(O)), C1x(l) = −C2g(l, x(l), y(l)),where Q, Bi, Ci, i = 1, 2, are n x n real matrices. An application is given to the second order equation xn = h(t, x, x') subject to certain nonlinear boundary conditions.
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Amodio, Pierluigi, Luigi Brugnano, and Felice Iavernaro. "Energy-conserving methods for Hamiltonian boundary value problems and applications in astrodynamics." Advances in Computational Mathematics 41, no. 4 (November 14, 2014): 881–905. http://dx.doi.org/10.1007/s10444-014-9390-z.

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Al-Hawasy, Jamil A. Ali. "The Continuous Classical Boundary Optimal Control of Couple Nonlinear Hyperbolic Boundary Value Problem with Equality and Inequality Constraints." Baghdad Science Journal 16, no. 4(Suppl.) (December 18, 2019): 1064. http://dx.doi.org/10.21123/bsj.2019.16.4(suppl.).1064.

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The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the state constrained problem are stated and proved.
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Al-Hawasy, Jamil A. Ali, and Lamyaa H. Ali. "Constraints Optimal Control Governing by Triple Nonlinear Hyperbolic Boundary Value Problem." Journal of Applied Mathematics 2020 (April 10, 2020): 1–14. http://dx.doi.org/10.1155/2020/8021635.

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The focus of this work lies on proving the existence theorem of a unique state vector solution (Stvs) of the triple nonlinear hyperbolic boundary value problem (TNHBVP) when the classical continuous control vector (CCCVE) is fixed by using the Galerkin method (Galm), proving the existence theorem of a unique constraints classical continuous optimal control vector (CCCOCVE) with vector state constraints (equality EQVC and inequality INEQVC). Also, it consists of studying for the existence and uniqueness adjoint vector solution (Advs) of the triple adjoint vector equations (TAEqs) associated with the considered triple state equations (Tsteqs). The Fréchet Derivative (Frde.) of the Hamiltonian (HAM) is found. At the end, the theorems for the necessary conditions and the sufficient conditions of optimality (Necoop and Sucoop) are achieved.
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Song, Mingliang, and Shuyuan Mei. "Existence of Three Solutions for Nonlinear Operator Equations and Applications to Second-Order Differential Equations." Journal of Function Spaces 2021 (January 28, 2021): 1–17. http://dx.doi.org/10.1155/2021/6668037.

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The existence of three solutions for nonlinear operator equations is established via index theory for linear self-adjoint operator equations, critical point reduction method, and three critical points theorems obtained by Brezis-Nirenberg, Ricceri, and Averna-Bonanno. Applying the results to second-order Hamiltonian systems satisfying generalized periodic boundary conditions or Sturm-Liouville boundary conditions and elliptic partial differential equations satisfying Dirichlet boundary value conditions, we obtain some new theorems concerning the existence of three solutions.
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Brugnano, Luigi, Gianluca Frasca-Caccia, and Felice Iavernaro. "Line Integral Solution of Hamiltonian PDEs." Mathematics 7, no. 3 (March 18, 2019): 275. http://dx.doi.org/10.3390/math7030275.

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In this paper, we report on recent findings in the numerical solution of Hamiltonian Partial Differential Equations (PDEs) by using energy-conserving line integral methods in the Hamiltonian Boundary Value Methods (HBVMs) class. In particular, we consider the semilinear wave equation, the nonlinear Schrödinger equation, and the Korteweg–de Vries equation, to illustrate the main features of this novel approach.
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Amodio, Pierluigi, Luigi Brugnano, and Felice Iavernaro. "Continuous-Stage Runge–Kutta Approximation to Differential Problems." Axioms 11, no. 5 (April 21, 2022): 192. http://dx.doi.org/10.3390/axioms11050192.

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In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Such methods admit an interesting interpretation in terms of continuous-stage Runge–Kutta methods. In this review paper, we recall this aspect and extend it to higher-order differential problems.
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Dissertations / Theses on the topic "Hamiltonian Boundary Value Method"

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Heredia, N. Fernando. "A new method for boundary value problems." Thesis, Monterey, California. Naval Postgraduate School, 1985. http://hdl.handle.net/10945/21467.

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Rockstroh, Parousia. "Boundary value problems for the Laplace equation on convex domains with analytic boundary." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273939.

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In this thesis we study boundary value problems for the Laplace equation on do mains with smooth boundary. Central to our analysis is a relation, known as the global relation, that couples the boundary data for a given BVP. Previously, the global re lation has primarily been applied to elliptic PDEs defined on polygonal domains. In this thesis we extend the use of the global relation to domains with smooth boundary. This is done by introducing a new transform, denoted by F_p, that is an analogue of the Fourier transform on smooth convex curves. We show that the F_p-transform is a bounded and invertible integral operator. Following this, we show that the F_p-transform naturally arises in the global relation for the Laplace equation on domains with smooth boundary. Using properties of the F_p-transform, we show that the global relation defines a continuously invertible map between the Dirichlet and Neumann data for a given BVP for the Laplace equation. Following this, we construct a numerical method that uses the global relation to find the Neumann data, given the Dirichlet data, for a given BVP for the Laplace equation on a domain with smooth boundary.
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Ugail, Hassan. "Method of boundary based smooth shape design." ACTA Press, 2005. http://hdl.handle.net/10454/2685.

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The discussion in this paper focuses on how boundary based smooth shape design can be carried out. For this we treat surface generation as a mathematical boundary-value problem. In particular, we utilize elliptic Partial Differential Equations (PDEs) of arbitrary order. Using the methodology outlined here a designer can therefore generate the geometry of shapes satisfying an arbitrary set of boundary conditions. The boundary conditions for the chosen PDE can be specified as curves in 3-space defining the profile geometry of the shape. We show how a compact analytic solution for the chosen arbitrary order PDE can be formulated enabling complex shapes to be designed and manipulated in real time. This solution scheme, although analytic, satisfies exactly, even in the case of general boundary conditions, where the resulting surface has a closed form representation allowing real time shape manipulation. In order to enable users to appreciate the powerful shape design and manipulation capability of the method, we present a set of practical examples.
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Chan, Kwok Cheung. "Shooting method for singularly perturbed two-point boundary value problems." HKBU Institutional Repository, 1998. http://repository.hkbu.edu.hk/etd_ra/274.

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Bozkaya, Canan. "Boundary Element Method Solution Of Initial And Boundary Value Problems In Fluid Dynamics And Magnetohydrodynamics." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609552/index.pdf.

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In this thesis, the two-dimensional initial and boundary value problems invol-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions with mixed boundary conditions are obtained for high values of Hartmann number, M. For the solution of transient convection-diffusion type equations the dual reciprocity boundary element method (DRBEM) in space is combined with the differential quadrature method (DQM) in time. The DRBEM is applied with the fundamental solution of Laplace equation treating all the other terms in the equation as nonhomogeneity. The use of DQM eliminates the need of iteration and very small time increments since it is unconditionally stable. Applications include unsteady MHD duct flow and elastodynamic problems. The transient Navier-Stokes equations which are nonlinear in nature are also solved with the DRBEM in space - DQM in time procedure iteratively in terms of stream function and vorticity. The procedure is applied to the lid-driven cavity flow for moderate values of Reynolds number. The natural convection cavity flow problem is also solved for high values of Rayleigh number when the energy equation is added.
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Alsaedy, Ammar, and Nikolai Tarkhanov. "The method of Fischer-Riesz equations for elliptic boundary value problems." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6179/.

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We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.
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Mokhtarzadeh, M. R. "A general global approximation method for the solution of boundary value problems." Thesis, Loughborough University, 1998. https://dspace.lboro.ac.uk/2134/14478.

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A general global approximation scheme is developed and its generality is demonstrated by the derivation of classical Lagrange and Hermite interpolation and finite difference and finite element approximations as its special cases. It is also shown that previously reported general approximation techniques which use the idea of moving least square are also special cases of the present method. The combination of the developed general global approximation technique with the weighted residual methods provides a very powerful scheme for the solution of the boundary value problems formulated in terms of differential equations. Although this application is the main purpose of the this project, nevertheless, the power and flexibility of the developed approximation allows it to be used in many other areas. In this study the following applications of the described approximation are developed: 1- data fitting (including curve and surface fitting) 2- plane mapping (both in cases where a conformal mapping exists and for non-conformal mapping) 3- solution of eigenvalue problems with particular application to spectral expansions used in the modal representation of shallow water equations 4- solution of ordinary differential equations (including Sturm-Liouville equations, non-homogeneous equations with non-smooth right hand sides and 4th order equations) 5- elliptic partial differential equations (including Poisson equations with non-smooth right hand sides) A computer program which can handle the above applications is developed. This program utilises symbolic, numerical and graphical and the programming language provided by the Mathematica package.
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Chibi, Ahmed-Salah. "Defect correction and Galerkin's method for second-order elliptic boundary value problems." Thesis, Imperial College London, 1989. http://hdl.handle.net/10044/1/47378.

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Yang, Zhiyun. "A Cartesian grid method for elliptic boundary value problems in irregular regions /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/6759.

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Poullikkas, Andreas. "The Method of Fundamental Solutions for the solution of elliptic boundary value problems." Thesis, Loughborough University, 1997. https://dspace.lboro.ac.uk/2134/27141.

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We investigate the use of the Method of Fundamental Solutions (MFS) for the numerical solution of elliptic problems arising in engineering. In particular, we examine harmonic and biharmonic problems with boundary singularities, certain steady-state free boundary flow problems and inhomogeneous problems. The MFS can be viewed as an indirect boundary method with an auxiliary boundary. The solution is approximated by a linear combination of fundamental solutions of the governing equation which are expressed in terms of sources located outside the domain of the problem. The unknown coefficients in the linear combination of fundamental solutions and the location of the sources are determined so that the boundary conditions are satisfied in a least squares sense. The MFS shares the same advantages of the boundary methods over domain discretisation methods. Moreover, it is relatively easy to implement, it is adaptive in the sense that it takes into account sharp changes in the solution and/or in the geometry of the domain and it can easily incorporate complicated boundary conditions.
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Books on the topic "Hamiltonian Boundary Value Method"

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N, Fernando Heredia. A new method for boundary value problems. Monterey, California: Naval Postgraduate School, 1985.

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Surana, Karan S., and J. N. Reddy. The Finite Element Method for Boundary Value Problems. Boca Raton : CRC Press, 2017.: CRC Press, 2016. http://dx.doi.org/10.1201/9781315365718.

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Natural boundary integral method and its applications. Beijing: Science Press, 2002.

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Sabelʹfelʹd, K. K. Monte Carlo methods in boundary value problems. Berlin: Springer-Verlag, 1991.

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Schwarz, Günter. Hodge decomposition: A method for solving boundary value problems. Berlin: Springer-Verlag, 1995.

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Schwarz, Günter. Hodge Decomposition—A Method for Solving Boundary Value Problems. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/bfb0095978.

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Hodge decomposition: A method for solving boundary value problems. Berlin: Springer, 1995.

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Vasilʹeva, A. B. The boundary function method for singular perturbation problems. Philadelphia: Society for Industrial and Applied Mathematics, 1995.

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Raamachandran, J. Boundary and finite elements theory and problems. Boca Raton, Fla: CRC Press, 2000.

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Lingju, Kong, ed. Multiple solutions of boundary value problems: A variational approach. New Jersey: World Scientific, 2016.

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Book chapters on the topic "Hamiltonian Boundary Value Method"

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Papageorgiou, Nikolaos S., and Sophia Th Kyritsi-Yiallourou. "Boundary Value Problems–Hamiltonian Systems." In Advances in Mechanics and Mathematics, 351–454. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/b120946_5.

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Kolokoltsov, Vassili N. "Boundary value problem for Hamiltonian systems." In Lecture Notes in Mathematics, 40–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/bfb0112491.

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Krall, Allan M. "Regular Linear Hamiltonian Systems." In Hilbert Space, Boundary Value Problems and Orthogonal Polynomials, 51–72. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8155-5_4.

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Keskin, Ali Ümit. "Adomian Decomposition Method (ADM)." In Boundary Value Problems for Engineers, 311–59. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21080-9_7.

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Krall, Allan M. "The Niessen Approach to Singular Hamiltonian Systems." In Hilbert Space, Boundary Value Problems and Orthogonal Polynomials, 87–106. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8155-5_6.

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Bellen, A. "A Runge-Kutta-Nystrom Method for Delay Differential Equations." In Numerical Boundary Value ODEs, 271–83. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5160-6_16.

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Brown, David L. "A Numerical Method for Singular Perturbation Problems with Turning Points." In Numerical Boundary Value ODEs, 193–205. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5160-6_11.

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Polycarpou, Anastasis C. "Two-Dimensional Boundary-Value Problems." In Introduction to the Finite Element Method in Electromagnetics, 51–114. Cham: Springer International Publishing, 2006. http://dx.doi.org/10.1007/978-3-031-01689-9_2.

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Polycarpou, Anastasis C. "One-Dimensional Boundary-Value Problems." In Introduction to the Finite Element Method in Electromagnetics, 1–49. Cham: Springer International Publishing, 2006. http://dx.doi.org/10.1007/978-3-031-01689-9_1.

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Markowich, Peter A. "A Finite Difference Method for the Basic Stationary Semiconductor Device Equations." In Numerical Boundary Value ODEs, 285–301. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5160-6_17.

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Conference papers on the topic "Hamiltonian Boundary Value Method"

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Iavernaro, Felice, and Brigida Pace. "Conservative Block‐Boundary Value Methods for the Solution of Polynomial Hamiltonian Systems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991075.

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Barletti, L., L. Brugnano, G. Frasca Caccia, and F. Iavernaro. "Solving the nonlinear Schrödinger equation using energy conserving Hamiltonian boundary value methods." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992336.

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Reyhart, Delon, and Sohel Anwar. "Optimal Control of a Quasi-Linearized On Demand All Wheel Drive System." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-69104.

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This paper presents an optimal algorithm to enhance the performance of an On-demand All Wheel Drive (ODAWD) vehicle by traction improvement through regulation of wheel slip. A “Minimum Fuel Problem” is developed with a cost function minimizing the slip error and the control action which is the ratio of the torque transmitted to the non driven wheels (rear wheels) to the total torque from engine. A simplified vehicle model (bicycle model) is used for the derivation and the system produces a Two Point Boundary Value Problem (TPBVP) once the Hamiltonian is formed and Pontryagin minimum Principle is used. An iterative algorithm based on the “Shooting Method” is then used to arrive at the optimal control action. The proposed controller optimally reduces the wheel slip error by engaging and dynamically controlling a hydraulic clutch which transmits the optimal torque to the rear wheels, thus reducing the vehicle longitudinal slip and enhancing vehicle traction. The controller was simulated in two phases where the first phase was an open loop simulation for a desired vehicle speed profile and the second phase, a closed loop system where the controller was integrated on a validated 14 degree-of-freedom detailed vehicle model in SIMULINK. The two phased simulation results provide high promise of the controller performance on low friction coefficient surfaces with enhanced traction and reduced vehicle longitudinal slip in an acceleration event.
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Darrall, Bradley T., and Gary F. Dargush. "Mixed Convolved Action Principles for Dynamics of Linear Poroelastic Continua." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52728.

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Although Lagrangian and Hamiltonian analytical mechanics represent perhaps the most remarkable expressions of the dynamics of a mechanical system, these approaches also come with limitations. In particular, there is inherent difficulty to represent dissipative processes and the restrictions placed on end point variations are not consistent with the definition of initial value problems. The present work on poroelastic media extends the recent formulation of a mixed convolved action to address a continuum dynamical problem with dissipation through the development of a new variational approach. The action in this proposed approach is formed by replacing the inner product in Hamilton’s principle with a time convolution. As a result, dissipative processes can be represented in a natural way and the required constraints on the variations are consistent with the actual initial and boundary conditions of the problem. The variational formulations developed here employ temporal impulses of velocity, effective stress, pore pressure and pore fluid mass flux as primary variables in this mixed approach, which also uses convolution operators and fractional calculus to achieve the desired characteristics. The resulting mixed convolved action is formulated in both the time and frequency domains to develop two new stationary principles for dynamic poroelasticity. In addition, the first variation of the action provides a temporally well-balanced weak form that leads to a new family of finite element methods in time, as well as space.
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Bin, Honghua, and Zhenkun Huang. "Boundary Value Problems for Discrete Hamiltonian Systems with Forcing Terms." In 2009 WRI World Congress on Software Engineering. IEEE, 2009. http://dx.doi.org/10.1109/wcse.2009.70.

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Amodio, Pierluigi, Luigi Brugnano, and Felice Iavernaro. "Energy conservation in the numerical solution of Hamiltonian boundary value problems." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825414.

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GNITKO, VASYL I., ARTEM O. KARAIEV, NEELAM CHOUDHARY, and ELENA A. STRELNIKOVA. "BOUNDARY ELEMENT METHOD ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS." In BEM/MRM44. Southampton UK: WIT Press, 2021. http://dx.doi.org/10.2495/be440031.

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Kovač, N., D. Poljak, S. Kraljević, and B. Jajac. "Computation of maximal electric field value generated by a power substation." In BOUNDARY ELEMENT METHOD 2006. Southampton, UK: WIT Press, 2006. http://dx.doi.org/10.2495/be06017.

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KURYLEV, Y. "MOMENTS' METHOD FOR INVERSE BOUNDARY VALUE PROBLEMS." In Proceedings of the Sixth International Workshop. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702593_0034.

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Kun Fu, You-Hua Wang, Yong-Feng Dong, Xiang-Dan Hou, Xue-Qin Shen, and Wei-Li Yan. "Support vector regression method for boundary value problems." In Proceedings of 2005 International Conference on Machine Learning and Cybernetics. IEEE, 2005. http://dx.doi.org/10.1109/icmlc.2005.1527692.

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Reports on the topic "Hamiltonian Boundary Value Method"

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Shani, Uri, Lynn Dudley, Alon Ben-Gal, Menachem Moshelion, and Yajun Wu. Root Conductance, Root-soil Interface Water Potential, Water and Ion Channel Function, and Tissue Expression Profile as Affected by Environmental Conditions. United States Department of Agriculture, October 2007. http://dx.doi.org/10.32747/2007.7592119.bard.

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Constraints on water resources and the environment necessitate more efficient use of water. The key to efficient management is an understanding of the physical and physiological processes occurring in the soil-root hydraulic continuum.While both soil and plant leaf water potentials are well understood, modeled and measured, the root-soil interface where actual uptake processes occur has not been sufficiently studied. The water potential at the root-soil interface (yᵣₒₒₜ), determined by environmental conditions and by soil and plant hydraulic properties, serves as a boundary value in soil and plant uptake equations. In this work, we propose to 1) refine and implement a method for measuring yᵣₒₒₜ; 2) measure yᵣₒₒₜ, water uptake and root hydraulic conductivity for wild type tomato and Arabidopsis under varied q, K⁺, Na⁺ and Cl⁻ levels in the root zone; 3) verify the role of MIPs and ion channels response to q, K⁺ and Na⁺ levels in Arabidopsis and tomato; 4) study the relationships between yᵣₒₒₜ and root hydraulic conductivity for various crops representing important botanical and agricultural species, under conditions of varying soil types, water contents and salinity; and 5) integrate the above to water uptake term(s) to be implemented in models. We have made significant progress toward establishing the efficacy of the emittensiometer and on the molecular biology studies. We have added an additional method for measuring ψᵣₒₒₜ. High-frequency water application through the water source while the plant emerges and becomes established encourages roots to develop towards and into the water source itself. The yᵣₒₒₜ and yₛₒᵢₗ values reflected wetting and drying processes in the rhizosphere and in the bulk soil. Thus, yᵣₒₒₜ can be manipulated by changing irrigation level and frequency. An important and surprising finding resulting from the current research is the obtained yᵣₒₒₜ value. The yᵣₒₒₜ measured using the three different methods: emittensiometer, micro-tensiometer and MRI imaging in both sunflower, tomato and corn plants fell in the same range and were higher by one to three orders of magnitude from the values of -600 to -15,000 cm suggested in the literature. We have added additional information on the regulation of aquaporins and transporters at the transcript and protein levels, particularly under stress. Our preliminary results show that overexpression of one aquaporin gene in tomato dramatically increases its transpiration level (unpublished results). Based on this information, we started screening mutants for other aquaporin genes. During the feasibility testing year, we identified homozygous mutants for eight aquaporin genes, including six mutants for five of the PIP2 genes. Including the homozygous mutants directly available at the ABRC seed stock center, we now have mutants for 11 of the 19 aquaporin genes of interest. Currently, we are screening mutants for other aquaporin genes and ion transporter genes. Understanding plant water uptake under stress is essential for the further advancement of molecular plant stress tolerance work as well as for efficient use of water in agriculture. Virtually all of Israel’s agriculture and about 40% of US agriculture is made possible by irrigation. Both countries face increasing risk of water shortages as urban requirements grow. Both countries will have to find methods of protecting the soil resource while conserving water resources—goals that appear to be in direct conflict. The climate-plant-soil-water system is nonlinear with many feedback mechanisms. Conceptual plant uptake and growth models and mechanism-based computer-simulation models will be valuable tools in developing irrigation regimes and methods that maximize the efficiency of agricultural water. This proposal will contribute to the development of these models by providing critical information on water extraction by the plant that will result in improved predictions of both water requirements and crop yields. Plant water use and plant response to environmental conditions cannot possibly be understood by using the tools and language of a single scientific discipline. This proposal links the disciplines of soil physics and soil physical chemistry with plant physiology and molecular biology in order to correctly treat and understand the soil-plant interface in terms of integrated comprehension. Results from the project will contribute to a mechanistic understanding of the SPAC and will inspire continued multidisciplinary research.
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