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Готові списки джерел за темами / Differential equations, Partial Numerical solutions

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Добірка наукової літератури з теми "Differential equations, Partial Numerical solutions"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 1 серпня 2024

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Статті в журналах з теми "Differential equations, Partial Numerical solutions"

1

ALdarawi, Iman, Banan Maayah, Eman Aldabbas, and Eman Abuteen. "Numerical Solutions of Some Classes of Partial Differential Equations of Fractional Order." European Journal of Pure and Applied Mathematics 16, no. 4 (October 30, 2023): 2132–44. http://dx.doi.org/10.29020/nybg.ejpam.v16i4.4928.

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This paper explores the solutions of certain fractional partial differential equations using two methods; the first method involves separation of variables, which is a common technique for solving partial differential equations. However, since many equations cannot be separated in this way, the tensor product of Banach spaces method is applied to find the atomic solutions. To solve the resulting ordinary differential equations, the reproducing Kernel Hilbert space method is used to find numerical solutions, which are then used to find the numerical solution of the partial differential equation. The residual errors indicate that this method is effective and powerful. In summary, this paper presents a study on the solutions of certain fractional partial differential equations using two methods and demonstrates the effectiveness of these methods in finding numerical solutions.

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2

NAKAO, Mitsuhiro. "Numerical Verification of Solutions for Partial Differential Equations." IEICE ESS FUNDAMENTALS REVIEW 2, no. 3 (2009): 19–28. http://dx.doi.org/10.1587/essfr.2.3_19.

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3

Nakao, Mitsuhiro T. "Numerical verification for solutions to partial differential equations." Sugaku Expositions 30, no. 1 (March 17, 2017): 89–109. http://dx.doi.org/10.1090/suga/419.

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4

Wu, G., Eric Wai Ming Lee, and Gao Li. "Numerical solutions of the reaction-diffusion equation." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 2 (March 2, 2015): 265–71. http://dx.doi.org/10.1108/hff-04-2014-0113.

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Purpose – The purpose of this paper is to introduce variational iteration method (VIM) to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations. The Lagrange multipliers become the integral kernels. Design/methodology/approach – Using the discrete numerical integral formula, the general way is given to solve the famous reaction-diffusion equation numerically. Findings – With the given explicit solution, the results show the conveniences of the general numerical schemes and numerical simulation of the reaction-diffusion is finally presented in the cases of various coefficients. Originality/value – The method avoids the treatment of the time derivative as that in the classical finite difference method and the VIM is introduced to construct equivalent integral equations for initial-boundary value problems of nonlinear partial differential equations.

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5

Kurbonov, Elyorjon, Nodir Rakhimov, Shokhabbos Juraev, and Feruza Islamova. "Derive the finite difference scheme for the numerical solution of the first-order diffusion equation IBVP using the Crank-Nicolson method." E3S Web of Conferences 402 (2023): 03029. http://dx.doi.org/10.1051/e3sconf/202340203029.

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In the article, a differential scheme is created for the the first-order diffusion equation using the Crank-Nicolson method. The stability of the differential scheme was checked using the Neumann method. To solve the problem numerically, stability intervals were found using the Neman method. This work presents an analysis of the stability of the Crank-Nicolson scheme for the two-dimensional diffusion equation using Von Neumann stability analysis. The Crank-Nicolson scheme is a widely used numerical method for solving partial differential equations that combines the explicit and implicit schemes. The stability analysis is an important factor to consider when choosing a numerical method for solving partial differential equations, as numerical instability can cause inaccurate solutions. We show that the Crank-Nicolson scheme is unconditionally stable, meaning that it can be used for a wide range of parameters without being affected by numerical instability. Overall, the analysis and implementation presented in this work provide a framework for designing and analyzing numerical methods for solving partial differential equations using the Crank-Nicolson scheme. The stability analysis is crucial for ensuring the accuracy and reliability of numerical solutions of partial differential equations.

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6

Balamuralitharan, S., and . "MATLAB Programming of Nonlinear Equations of Ordinary Differential Equations and Partial Differential Equations." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 773. http://dx.doi.org/10.14419/ijet.v7i4.10.26114.

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My idea of this paper is to discuss the MATLAB program for various mathematical modeling in ordinary differential equations (ODEs) and partial differential equations (PDEs). Idea of this paper is very useful to research scholars, faculty members and all other fields like engineering and biology. Also we get easily to find the numerical solutions from this program.

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7

Zhang, Zhao. "Numerical Analysis and Comparison of Gridless Partial Differential Equations." International Journal of Circuits, Systems and Signal Processing 15 (August 31, 2021): 1223–31. http://dx.doi.org/10.46300/9106.2021.15.133.

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In the field of science and engineering, partial differential equations play an important role in the process of transforming physical phenomena into mathematical models. Therefore, it is very important to get a numerical solution with high accuracy. In solving linear partial differential equations, meshless solution is a very important method. Based on this, we propose the numerical solution analysis and comparison of meshless partial differential equations (PDEs). It is found that the interaction between the numerical solutions of gridless PDEs is better, and the absolute error and relative error are lower, which proves the superiority of the numerical solutions of gridless PDEs

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8

Zou, Guang-an. "Numerical solutions to time-fractional stochastic partial differential equations." Numerical Algorithms 82, no. 2 (November 5, 2018): 553–71. http://dx.doi.org/10.1007/s11075-018-0613-0.

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9

Secer, Aydin. "Sinc-Galerkin method for solving hyperbolic partial differential equations." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 8, no. 2 (July 24, 2018): 250–58. http://dx.doi.org/10.11121/ijocta.01.2018.00608.

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In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically.

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10

Wang, Zhigang, Xiaoting Liu, Lijun Su, and Baoyan Fang. "Numerical Solutions of Convective Diffusion Equations using Wavelet Collocation Method." Advances in Engineering Technology Research 1, no. 1 (May 17, 2022): 192. http://dx.doi.org/10.56028/aetr.1.1.192.

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Some partial differential equations appear in many application fields. Therefore, the discussion of numerical solutions of those partial differential equations using numerical methods becomes a valuable and important issue in numerical simulation. In numerical methods, the wavelet-collocation method has been frequently developed for solving PDEs, and the algorithm has yielded substantial results. However, theoretical research of the numerical solution has been rarely discussed yet. In this paper, the numerical solution of convective diffusion equations using the wavelet-collocation method is established, and its existence and uniqueness are derived.

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Дисертації з теми "Differential equations, Partial Numerical solutions"

1

Bratsos, A. G. "Numerical solutions of nonlinear partial differential equations." Thesis, Brunel University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332806.

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2

Sundqvist, Per. "Numerical Computations with Fundamental Solutions." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5757.

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3

Kwok, Ting On. "Adaptive meshless methods for solving partial differential equations." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1076.

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4

Zeng, Suxing. "Numerical solutions of boundary inverse problems for some elliptic partial differential equations." Morgantown, W. Va. : [West Virginia University Libraries], 2009. http://hdl.handle.net/10450/10345.

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Thesis (Ph. D.)--West Virginia University, 2009.
Title from document title page. Document formatted into pages; contains v, 58 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 56-58).

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5

Williamson, Rosemary Anne. "Numerical solution of hyperbolic partial differential equations." Thesis, University of Cambridge, 1985. https://www.repository.cam.ac.uk/handle/1810/278503.

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6

Postell, Floyd Vince. "High order finite difference methods." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/28876.

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7

Luo, Wuan Hou Thomas Y. "Wiener chaos expansion and numerical solutions of stochastic partial differential equations /." Diss., Pasadena, Calif. : Caltech, 2006. http://resolver.caltech.edu/CaltechETD:etd-05182006-173710.

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8

Cheung, Ka Chun. "Meshless algorithm for partial differential equations on open and singular surfaces." HKBU Institutional Repository, 2016. https://repository.hkbu.edu.hk/etd_oa/278.

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Анотація:

Radial Basis function (RBF) method for solving partial differential equation (PDE) has a lot of applications in many areas. One of the advantages of RBF method is meshless. The cost of mesh generation can be reduced by playing with scattered data. It can also allow adaptivity to solve some problems with special feature. In this thesis, RBF method will be considered to solve several problems. Firstly, we solve the PDEs on surface with singularity (folded surface) by a localized method. The localized method is a generalization of finite difference method. A priori error estimate for the discreitzation of Laplace operator is given for points selection. A stable solver (RBF-QR) is used to avoid ill-conditioning for the numerical simulation. Secondly, a {dollar}H^2{dollar} convergence study for the least-squares kernel collocation method, a.k.a. least-square Kansa's method will be discussed. This chapter can be separated into two main parts: constraint least-square method and weighted least-square method. For both methods, stability and consistency analysis are considered. Error estimate for both methods are also provided. For the case of weighted least-square Kansa's method, we figured out a suitable weighting for optimal error estimation. In Chapter two, we solve partial differential equation on smooth surface by an embedding method in the embedding space {dollar}\R^d{dollar}. Therefore, one can apply any numerical method in {dollar}\R^d{dollar} to solve the embedding problem. Thus, as an application of previous result, we solve embedding problem by least-squares kernel collocation. Moreover, we propose a new embedding condition in this chapter which has high order of convergence. As a result, we solve partial differential equation on smooth surface with a high order kernel collocation method. Similar to chapter two, we also provide error estimate for the numerical solution. Some applications such as pattern formation in the Brusselator system and excitable media in FitzHughNagumo model are also studied.

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9

Yang, Xue-Feng. "Extensions of sturm-liouville theory : nodal sets in both ordinary and partial differential equations." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/28021.

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10

He, Chuan. "Numerical solutions of differential equations on FPGA-enhanced computers." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1248.

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Книги з теми "Differential equations, Partial Numerical solutions"

1

W, Thomas J. Numerical partial differential equations. New York: Springer, 1995.

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2

Matthew, Witten, ed. Hyperbolic partial differential equations. Oxford: Pergamon Press, 1985.

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3

I, Hariharan S., and Moulden T. H. 1939-, eds. Numerical methods for partial differential equations. Harlow: Longman Scientific & Technical, 1986.

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4

Manuel, Castellet, Shu Chi-Wang, Russo Giovanni, Falletta Silvia, and SpringerLink (Online service), eds. Numerical Solutions of Partial Differential Equations. Basel: Birkhäuser Basel, 2009.

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5

Bertoluzza, Silvia, Giovanni Russo, Silvia Falletta, and Chi-Wang Shu. Numerical Solutions of Partial Differential Equations. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8940-6.

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6

E, Pearson Carl, ed. Partial differential equations: Theory and technique. 2nd ed. Boston: Academic Press, 1988.

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7

Morton, K. W. Numerical solution of partial differential equations. New York: Cambridge University Press, 1994.

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8

Lui, S. H. Numerical analysis of partial differential equations. Hoboken, N.J: Wiley, 2011.

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9

Matthew, Witten, ed. Hyperbolic partial differential equations II. New York: Oxford, 1985.

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10

1931-, Mayers D. F., ed. Numerical solution of partial differential equations. 2nd ed. Cambridge: Cambridge Univeristy Press, 2005.

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Частини книг з теми "Differential equations, Partial Numerical solutions"

1

Logan, J. David. "Numerical Computation of Solutions." In Applied Partial Differential Equations, 257–77. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12493-3_6.

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2

Bleecker, David, and George Csordas. "Numerical Solutions of PDEs — An Introduction." In Basic Partial Differential Equations, 503–58. Boston, MA: Springer US, 1992. http://dx.doi.org/10.1007/978-1-4684-1434-9_8.

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3

Stroud, K. A., and Dexter Booth. "Numerical solutions of partial differential equations." In Advanced Engineering Mathematics, 593–641. London: Macmillan Education UK, 2011. http://dx.doi.org/10.1057/978-0-230-34474-7_18.

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4

Saha Ray, Santanu. "Numerical Solutions of Partial Differential Equations." In Numerical Analysis with Algorithms and Programming, 591–640. Boca Raton : Taylor & Francis, 2016. | “A CRC title.”: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315369174-10.

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5

Fox, William P., and Richard D. West. "Numerical Solutions to Partial Differential Equations." In Numerical Methods and Analysis with Mathematical Modelling, 362–81. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781032703671-13.

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6

Leung, Anthony W. "Systems of Finite Difference Equations, Numerical Solutions." In Systems of Nonlinear Partial Differential Equations, 271–323. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-015-3937-1_6.

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7

Dong, Gang Nathan. "Numerical Solutions of Financial Partial Differential Equations." In Handbook of Quantitative Finance and Risk Management, 1209–21. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-0-387-77117-5_79.

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8

Saha Ray, Santanu. "Numerical Solutions of Riesz Fractional Partial Differential Equations." In Nonlinear Differential Equations in Physics, 119–54. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-1656-6_4.

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9

Dean, Edward J., and Roland Glowinski. "On the Numerical Solution of the Elliptic Monge—Ampère Equation in Dimension Two: A Least-Squares Approach." In Partial Differential Equations, 43–63. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8758-5_3.

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10

Pownuk, Andrzej. "Numerical solutions of fuzzy partial differential equations and its applications in computational mechanics." In Fuzzy Partial Differential Equations and Relational Equations, 308–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-39675-8_13.

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Тези доповідей конференцій з теми "Differential equations, Partial Numerical solutions"

1

Savaşaneril, Nurcan Baykuş. "Numerical Solutions of Hyperbolic Partial Differential Equations." In 7th International Students Science Congress. Izmir International guest Students Association, 2023. http://dx.doi.org/10.52460/issc.2023.033.

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Hyperbolic partial differential equations are frequently referenced in modeling real-world problems in mathematics and engineering. In this study, a matrix method based on collocation points and Taylor polynomials is presented to obtain the approximate solution of the hyperbolic partial differential equation. This technique reduces the solution of the mentioned hyperbolic partial differential equation under initial and boundary conditions to the solution of a matrix equation whose Taylor coefficients are unknown. Thus, the approximate solution is obtained in terms of Taylor polynomials. An example is provided to showcase the practical application of the technique. In addition, the numerical results obtained using these collocation points were compared with the table and figure. All numerical calculations were made on the computer using a program written in WOLFRAM MATHEMATICA 13.0.

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2

Siddique, Mohammad, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Symposium: Advances in the Numerical Solutions of Partial Differential Equations." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498011.

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3

Kudryashov, N. A., and A. K. Volkov. "Concatenons as the solutions for non-linear partial differential equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992559.

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4

Surana, K. S., and M. A. Bona. "Computations of Higher Class Solutions of Partial Differential Equations." In ASME 2001 Engineering Technology Conference on Energy. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/etce2001-17142.

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Abstract This paper presents a new computational strategy, computational framework and mathematical framework for numerical computations of higher class solutions of differential and partial differential equations. The approach presented here utilizes ‘strong forms’ of the governing differential equations (GDE’s) and least squares approach in constructing the integral form. The conventional, or currently used, approaches seek the convergence of a solution in a fixed (order) space by h, p or hp-adaptive processes. The fundamental point of departure in the proposed approach is that we seek convergence of the computed solution by changing the orders of the spaces of the basis functions. With this approach convergence rates much higher than those from h,p–processes are achievable and the progressively computed solutions converge to the ‘strong’ i.e. ‘theoretical’ solutions of the GDE’s. Many other benefits of this approach are discussed and demonstrated. Stationary and time-dependant convection-diffusion and Burgers equations are used as model problems.

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5

Aleixo, Rafael, and Daniela Amazonas. "Noise Reduction on Numerical Solutions of Partial Differential Equations using Fuzzy Transform." In CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2018. http://dx.doi.org/10.5540/03.2018.006.01.0402.

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6

Nečasová, Gabriela, and Václav Šátek. "Taylor series based parallel numerical solution of partial differential equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0162190.

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7

Ashyralyev, Allaberen, Evren Hincal, and Bilgen Kaymakamzade. "Numerical solutions of the system of partial differential equations for observing epidemic models." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5049044.

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8

Liu, Zhiquan, Yu Liu, Dayou Lu, Yayu Yang, and Rui Fan. "Transmission Line Differential Protection Based on Numerical Solution of Partial Differential Equations." In 2023 IEEE International Conference on Advanced Power System Automation and Protection (APAP). IEEE, 2023. http://dx.doi.org/10.1109/apap59666.2023.10348502.

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9

Barletti, Luigi, Luigi Brugnano, Gianluca Frasca Caccia, and Felice Iavernaro. "Recent advances in the numerical solution of Hamiltonian partial differential equations." In NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”. Author(s), 2016. http://dx.doi.org/10.1063/1.4965308.

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10

Nečasová, Gabriela, Petr Veigend, and Václav Šátek. "Parallel solution of partial differential equations using the Taylor series method." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0082209.

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Звіти організацій з теми "Differential equations, Partial Numerical solutions"

1

Levine, Howard A. Numerical Solution of Ill Posed Problems in Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1987. http://dx.doi.org/10.21236/ada189383.

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2

Levine, Howard A. Numerical Solution of I11 Posed Problems in Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, November 1985. http://dx.doi.org/10.21236/ada162378.

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3

Levine, Howard A. Numerical Solution of Ill Posed Problems in Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, April 1985. http://dx.doi.org/10.21236/ada166096.

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4

Sharan, M., E. J. Kansa, and S. Gupta. Application of multiquadric method for numerical solution of elliptic partial differential equations. Office of Scientific and Technical Information (OSTI), January 1994. http://dx.doi.org/10.2172/10156506.

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5

Dupont, Todd F. Some Investigations into Variable Meshes for Numerical Solution of Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, May 1986. http://dx.doi.org/10.21236/ada168977.

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6

Oliker, V. I., and P. Waltman. New Methods for Numerical Solution of One Class of Strongly Nonlinear Partial Differential Equations with Applications. Fort Belvoir, VA: Defense Technical Information Center, January 1986. http://dx.doi.org/10.21236/ada186166.

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Oliker, V. I., and P. Waltman. New Methods for Numerical Solution of One Class of Strongly Nonlinear Partial Differential Equations with Applications. Fort Belvoir, VA: Defense Technical Information Center, August 1987. http://dx.doi.org/10.21236/ada189945.

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Trenchea, Catalin. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada567709.

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Trenchea, Catalin. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada577122.

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Sharp, D. H., S. Habib, and M. B. Mineev. Numerical Methods for Stochastic Partial Differential Equations. Office of Scientific and Technical Information (OSTI), July 1999. http://dx.doi.org/10.2172/759177.

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