Relevant bibliographies by topics / Integro-Differential

Academic literature on the topic 'Integro-Differential'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Integro-Differential"

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Parasidis, I. N. "EXTENSION AND DECOMPOSITION METHOD FOR DIFFERENTIAL AND INTEGRO-DIFFERENTIAL EQUATIONS." Eurasian Mathematical Journal 10, no. 3 (2019): 48–67. http://dx.doi.org/10.32523/2077-9879-2019-10-3-48-67.

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Guo, Li, Georg Regensburger, and Markus Rosenkranz. "On integro-differential algebras." Journal of Pure and Applied Algebra 218, no. 3 (March 2014): 456–73. http://dx.doi.org/10.1016/j.jpaa.2013.06.015.

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TÖRÖK, LEVENTE, and LÁSZLÓ B. KISH. "INTEGRO-DIFFERENTIAL STOCHASTIC RESONANCE." Fluctuation and Noise Letters 05, no. 01 (March 2005): L27—L42. http://dx.doi.org/10.1142/s0219477505002380.

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A new class of stochastic resonator (SRT) and Stochastic Resonance (SR) phenomena are described. The new SRT consist of a classical SRT, one or more time derivative circuits and the same number of time integrators. The incoming signal with additive noise is first time derivated, then passes through the classical SRT and finally it is time integrated. The resulting SR phenomena show a well defined SR. Moreover the signal transfer and SNR are the best at the high frequency end. A particular property of the new system is the much smoother output signal due to the time integration.
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Karkarashvili, G. S. "Fredholm integro-differential equation." Journal of Soviet Mathematics 66, no. 3 (September 1993): 2236–42. http://dx.doi.org/10.1007/bf01229590.

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Rangarajan, R., and Ananth Kumar S. R. "Homotopy-laplace Decomposition Method to Solve Nonlinear Differential-difference Equations." Journal of the Indian Mathematical Society 84, no. 3-4 (July 1, 2017): 255. http://dx.doi.org/10.18311/jims/2017/14928.

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In the recent literature, nonlinear differential equations, integro- differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the recent literature, nonlinear dierential equations, integro-differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the literature to solve above nonlinear problems. In the present paper a new method is proposed motivated by the above two methods to solve both nonlinear differential-difference equations and integro-differential-difference equations.
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Xu, Liguang, and András Prékopa. "L-operator integro-differential inequality for dissipativity of stochastic integro-differential equations." Mathematical Inequalities & Applications, no. 1 (2011): 123–34. http://dx.doi.org/10.7153/mia-14-10.

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Yuldashev, T. K., and S. K. Zarifzoda. "On a New Class of Singular Integro-differential Equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 101, no. 1 (March 30, 2021): 138–48. http://dx.doi.org/10.31489/2021m1/138-148.

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In this paper for a new class of model and non-model partial integro-differential equations with singularity in the kernel, we obtained integral representation of family of solutions by aid of arbitrary functions. Such type of integro-differential equations are different from Cauchy-type singular integro-differential equations. Cauchy-type singular integro-differential equations are studied by the methods of the theory of analytic functions. In the process of our research the new types of singular integro-differential operators are introduced and main property of entered operators are learned. It is shown that the solution of studied equation is equivalent to the solution of system of two equations with respect to x and y, one of which is integral equation and the other is integro-differential equation. Further, non-model integro-differential equations are studied by regularization method. This regularization method for non-model equation is based on selecting and analysis of a model part of the equation and reduced to the solution of two second kind Volterra type integral equations with weak singularity in the kernel. It is shown that the presence of a non-model part in the equation does not affect to the general structure of the solutions. From here investigation of the model equations for given class of the integro-differential equations becomes important. In the cases, when the solution of given integro-differential equation depends on any arbitrary functions, a Cauchy type problems are investigated.
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GIL', M. I. "POSITIVITY OF GREEN'S FUNCTIONS TO VOLTERRA INTEGRAL AND HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS." Analysis and Applications 07, no. 04 (October 2009): 405–18. http://dx.doi.org/10.1142/s0219530509001475.

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We consider Volterra integral equations and arbitrary order integro-differential equations. We establish positivity conditions and two-sided estimates for Green's functions. These results are then applied to obtain stability and positivity conditions for equations with nonlinear causal mappings (operators) and linear integro-differential parts. Such equations include differential, difference, differential-delay, integro-differential and other traditional equations.
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Alfredo Lorenzi. "OPERATOR EQUATIONS OF THE FIRST KIND AND INTEGRO-DIFFERENTIAL EQUATIONS OF DEGENERATE TYPE IN BANACH SPACES AND APPLICATIONS TO INTEGRO-DIFFERENTIAL PDE’S." Eurasian Journal of Mathematical and Computer Applications 1, no. 1 (2013): 50–75. http://dx.doi.org/10.32523/2306-3172-2013-1-2-50-75.

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Laoprasittichok, Sorasak, Sotiris K. Ntouyas, and Jessada Tariboon. "Hybrid fractional integro-differential inclusions." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 35, no. 2 (2015): 151. http://dx.doi.org/10.7151/dmdico.1174.

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Dissertations / Theses on the topic "Integro-Differential"

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Dareiotis, Anastasios Constantinos. "Stochastic partial differential and integro-differential equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14186.

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In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove existence and uniqueness of solutions of SPIDEs, we give a comparison principle and we suggest an approximation scheme for the non-local integral operators. Regarding SPDEs, we use techniques motivated by the work of De Giorgi, Nash, and Moser, in order to derive global and local supremum estimates, and a weak Harnack inequality.
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Stoleriu, Iulian. "Integro-differential equations in materials science." Thesis, University of Strathclyde, 2001. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=21413.

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This thesis deals with nonlocal models for solid-solid phase transitions, such as ferromagnetic phase transition or phase separation in binary alloys. We discuss here, among others, nonlocal versions of the Allen-Cahn and Cahn-Hilliard equations, as well as a nonlocal version of the viscous Cahn-Hilliard equation. The analysis of these models can be motivated by the fact that their local analogues fail to be applicable when the wavelength of microstructure is very small, e. g. at the nanometre scale. Though the solutions of these nonlocal equations and those of the local versions share some common properties, we find many differences between them, which are mainly due to the lack of compactness of the semigroups generated by nonlocal equations. Directly from microscopic considerations, we derive and analyse two new types of equations. One of the equations approximately represents the dynamic Ising model with vacancy-driven dynamics, and the other one is the vacancy-driven model obtained using the Vineyard formalism. These new equations are being put forward as possible improvements of the local and nonlocal Cahn-Hilliard models, as well as of the mean-field model for the Ising model with Kawasaki dynamics.
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Zhang, Wenkui. "Numerical analysis of delay differential and integro-differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0011/NQ42489.pdf.

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Roberts, Jason Anthony. "Numerical analysis of Volterra integro-differential equations." Thesis, University of Liverpool, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367635.

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Mansoora, Abida. "The sequential spectral method for integro-differential equations /." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=38230.

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Using the Galerkin method to solve nonlinear integro-differential equations of elliptic or parabolic type one needs to solve the resulting nonlinear systems of algebraic or ordinary differential equations. To solve these equations with Newtons method or a variant thereof can be very difficult and one needs a good initial guess for the methods to converge. Also there might be multiple solutions and it is virtually impossible to track all of them. In addition it is hard to study the parameter dependence of solutions. We developed a remedy for these problems by developing the sequential spectral method which avoids solving a nonlinear system altogether. In the sequential spectral method a scalar nonlinear algebraic or ordinary differential equation is solved at the initial stage and then the solution of the original problem is obtained through iterations, we never have to solve a nonlinear system at any stage of the method. The sequential spectral method converges linearly for steady state problems and superlinearly in the case of evolution. With the sequential spectral method we can obtain solutions to any desired accuracy with much less effort than with the Galerkin method. We can also increase the spectral degree of accuracy while the method is running. In addition one can easily detect the existence of multiple solutions by observing only a single equation and one can track those solutions. The behavior of the solution and the dependence on parameters can be estimated and one can also determine the blow up time for the corresponding parameter values by studying only a single equation. We further show that the sequential spectral method can be applied to a system of nonlinear elliptic partial differential equations.
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Ros, Xavier. "Integro-differential equations : regularity theory and Pohozaev identities." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/279289.

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The main topic of the thesis is the study of Elliptic PDEs. It is divided into three parts: (I) integro-differential equations, (II) stable solutions to reaction-diffusion problems, and (III) weighted isoperimetric and Sobolev inequalities. Integro-differential equations arise naturally in the study of stochastic processes with jumps, and are used in Finance, Physics, or Ecology. The most canonical example of integro-differential operator is the fractional Laplacian (the infinitesimal generator of the radially symmetric stable process). In the first Part of the thesis we find and prove the Pohozaev identity for such operator. We also obtain boundary regularity results for general integro-differential operators, as explained next. In the classical case of the Laplacian, the Pohozaev identity applies to any solution of linear or semilinear problems in bounded domains, and is a very important tool in the study of elliptic PDEs. Before our work, a Pohozaev identity for the fractional Laplacian was not known. It was not even known which form should it have, if any. In this thesis we find and establish such identity. Quite surprisingly, it involves a local boundary term, even though the operator is nonlocal. The proof of the identity requires fine boundary regularity properties of solutions, that we also establish here. Our boundary regularity results apply to fully nonlinear integro-differential equations, but they improve the best known ones even for linear ones. Our work in Part II concerns the regularity of local minimizers to some elliptic equations, a classical problem in the Calculus of Variations. More precisely, we study the regularity of stable solutions to reaction-diffusion problems in bounded domains. It is a long standing open problem to prove that all stable solutions are bounded, and thus regular, in dimensions n<10. In dimensions n>=10 there are examples of singular stable solutions. The question is still open in dimensions 4El tema principal de la tesi és l'estudi d'EDPs el·líptiques. La tesi està dividida en tres parts: (I) equacions integro-diferencials, (II) solucions estables de problemes de reacció-difusió, i (III) desigualtats isoperimètriques i de Sobolev amb pesos. Les equacions integro-differencials apareixen de manera natural en l'estudi de processos estocàstics amb salts (processos de Lévy), i s'utilitzen per modelitzar problemes en Finances, Física, o Ecologia. L'exemple més canònic d'operador integro-diferencial és el Laplacià fraccionari (el generador infinitesimal d'un procés estable i radialment simètric). A la Part I de la tesi trobem i demostrem la identitat de Pohozaev per aquest operador. També obtenim resultats de regularitat a la vora per operadors integro-diferencials més generals, tal com expliquem a continuació. En el cas clàssic del Laplacià, la identitat de Pohozaev s'aplica a qualsevol solució de problemes lineals o semilineals en dominis acotats, i és una eina molt important en l'estudi d'EDPs el·líptiques. Abans del nostre treball, no es coneixia cap identitat de Pohozaev pel Laplacià fraccionari. Ni tan sols es sabia quina forma hauria de tenir, en cas que existís. En aquesta tesi trobem i demostrem aquesta identitat. Sorprenentment, la identitat involucra un terma de vora local, tot i que l'operador és no-local. La demostració de la identitat requereix conèixer el comportament precís de les solucions a la vora, cosa que també obtenim aquí. Els nostres resultats de regularitat a la vora s'apliquen a equacions integro-diferencials completament no-lineals, però milloren els resultats anteriors fins i tot per a equacions lineals. A la Part II estudiem la regularitat dels minimitzants locals d'algunes equacions el·líptiques, un problema clàssic del Càlcul de Variacions. En concret, estudiem la regularitat de les solucions estables a problemes de reacció-difusió en dominis acotats. És un problema obert des de fa molts anys demostrar que totes les solucions estables són acotades (i per tant regulars) en dimensions n<10. En dimensions n>=10 hi ha exemples de solucions estables singulars. La questió encara està oberta en dimensions 4
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Parsons, Wade William. "Waveform relaxation methods for Volterra integro-differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0013/NQ52694.pdf.

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Athavale, Prashant Vinayak. "Novel integro-differential schemes for multiscale image representation." College Park, Md.: University of Maryland, 2009. http://hdl.handle.net/1903/9691.

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Thesis (Ph.D.) -- University of Maryland, College Park, 2009.
Thesis research directed by: Applied Mathematics & Statistics, and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Medlock, Jan P. "Integro-differential-equation models in ecology and epidemiology /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/6790.

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Lewis, Alexander M. (Alexander McDowell). "Positivity preserving solutions of partial integro-differential equations." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/51618.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2009.
"May 15th, 2009."
Includes bibliographical references (leaves 246-249).
Differential equations are one of the primary tools for modeling phenomena in chemical engineering. While solution methods for many of these types of problems are well-established, there is growing class of problems that lack standard solution methods: partial integro-differential equations. The primary challenges in solving these problems are due to several factors, such as large range of variables, non-local phenomena, multi-dimensionality, and physical constraints. All of these issues ultimately determine the accuracy and solution time for a given problem. Typical solution techniques are designed to handle every system using the same methods. And often the physical constraints of the problem are not addressed until after the solution is completed if at all. In the worst case this can lead to some problems being over-simplified and results that provide little physical insight. The general concept of exploiting solution domain knowledge can address these issues. Positivity and mass-conservation of certain quantities are two conditions that are difficult to achieve in standard numerical solution methods. However, careful design of the discretizations can achieve these properties with a negligible performance penalty. Another important consideration is the stability domain. The eigenvalues of the discretized problem put restrictions on the size of the time step. For "stiff' systems implicit methods are generally used but the necessary matrix inversions are costly, especially for equations with integral components. By better characterizing the system it is possible to use more efficient explicit methods.
(cont.) This work improves upon and combines several methods to develop more efficient methods. There are a vast number of systems that be solved using the methods developed in this work. The examples considered include population balances, neural models, radiative heat transfer models, among others. For the capstone portion, financial option pricing models using "jump-diffusion" motion are considered. Overall, gains in accuracy and efficiency were demonstrated across many conditions.
by Alexander M. Lewis.
Ph.D.
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Books on the topic "Integro-Differential"

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Lakshmikantham, V. Theory of integro-differential equations. Lausanne, Switzerland: Gordon and Breach Science Publishers, 1995.

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Grigoriev, Yurii N., Nail H. Ibragimov, Vladimir F. Kovalev, and Sergey V. Meleshko. Symmetries of Integro-Differential Equations. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-3797-8.

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1952-, Kalitvin Anatolij S., and Zabreĭko P. P. 1939-, eds. Partial integral operators and integro-differential equations. New York: M. Dekker, 2000.

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Singh, Harendra, Hemen Dutta, and Marcelo M. Cavalcanti, eds. Topics in Integral and Integro-Differential Equations. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-65509-9.

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Voronina, N. V. Integrodifferent︠s︡ialʹnye uravnenii︠a︡ i ikh prilozhenii︠a︡. Permʹ: Izd-vo Permskogo universiteta, 1995.

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Imanaliev, M. I. Nelineĭnye integro-differens͡s︡ialʹnye uravnenii͡a︡ s chastnymi proizvodnymi. Bishkek: "Ilim", 1992.

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Tang, Arsalang. Analysis and numerics of delay Volterra integro-differential equations. Manchester: University of Manchester, 1995.

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Billings, S. A. Mapping nonlinear integro-differential equations into the frequency domain. Sheffield: University of Sheffield, Dept. of Control Engineering, 1989.

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Garroni, M. G. Green functions for second order parabolic integro-differential problems. Burnt Mill, Harlow, Essex, England: Longman Scientific & Technical, 1992.

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Theory of functionals and of integral and integro-differential equations. Mineola, N.Y: Dover Publications, 2005.

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Book chapters on the topic "Integro-Differential"

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Das, Tapan Kumar. "Integro-Differential Equation." In Theoretical and Mathematical Physics, 125–39. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2361-0_9.

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Leonov, Gennadij A., Volker Reitmann, and Vera B. Smirnova. "Integro-Differential Equations." In Non-Local Methods for Pendulum-Like Feedback Systems, 171–88. Wiesbaden: Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-663-12261-6_8.

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Diagana, Toka. "Fractional Integro-Differential Equations." In Semilinear Evolution Equations and Their Applications, 97–111. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00449-1_7.

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Brunner, Hermann. "Integro-Differential Equations: Computation." In Encyclopedia of Applied and Computational Mathematics, 694–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_303.

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Wazwaz, Abdul-Majid. "Volterra Integro-Differential Equations." In Linear and Nonlinear Integral Equations, 175–212. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_5.

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Wazwaz, Abdul-Majid. "Fredholm Integro-Differential Equations." In Linear and Nonlinear Integral Equations, 213–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_6.

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Georgiev, Svetlin G. "Generalized Volterra Integro-Differential Equations." In Integral Equations on Time Scales, 197–225. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-228-1_4.

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Wazwaz, Abdul-Majid. "Volterra-Fredholm Integro-Differential Equations." In Linear and Nonlinear Integral Equations, 285–309. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_9.

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Chau, K. T. "Integral and Integro-Differential Equations." In Theory of Differential Equations in Engineering and Mechanics, 645–706. Boca Raton : CRC Press, [2017]: CRC Press, 2017. http://dx.doi.org/10.1201/9781315164939-11.

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Wazwaz, Abdul-Majid. "Nonlinear Volterra Integro-Differential Equations." In Linear and Nonlinear Integral Equations, 425–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21449-3_14.

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Conference papers on the topic "Integro-Differential"

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Torok, Levente, and Laszlo B. Kish. "Integro-differential stochastic resonance." In Second International Symposium on Fluctuations and Noise, edited by Derek Abbott, Sergey M. Bezrukov, Andras Der, and Angel Sanchez. SPIE, 2004. http://dx.doi.org/10.1117/12.548374.

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Rosenkranz, Markus, and Georg Regensburger. "Integro-differential polynomials and operators." In the twenty-first international symposium. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1390768.1390805.

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Domoshnitsky, Alexander I., and Yakov Goltser. "Hopf bifurcation of integro-differential equations." In The 6'th Colloquium on the Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, SZTE, 1999. http://dx.doi.org/10.14232/ejqtde.1999.5.3.

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Regensburger, Georg. "Symbolic Computation with Integro-Differential Operators." In ISSAC '16: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2930889.2930942.

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Slavova, Angela, and Zoya Zafirova. "Dynamic behavior of integro-differential CNN model." In PROCEEDINGS OF THE 44TH INTERNATIONAL CONFERENCE ON APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS: (AMEE’18). Author(s), 2018. http://dx.doi.org/10.1063/1.5082117.

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Belakroum, Dounia, and Kheireddine Belakroum. "Sinc approximation solution of integro-differential equation." In THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136180.

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DOMOSHNITSKY, ALEXANDER. "ON STABILITY OF NONAUTONOMOUS INTEGRO-DIFFERENTIAL EQUATIONS." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0180.

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Mehdiyeva, Galina, Vagif Ibrahimov, and Mehriban Imanova. "One relationship between Volterra integro-differential and ordinary differential equations." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114554.

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Mikaeilvand, Nasser, Sakineh Khakrangin, and Tofigh Allahviranloo. "Solving fuzzy Volterra integro-differential equation by fuzzy differential transform method." In 7th conference of the European Society for Fuzzy Logic and Technology. Paris, France: Atlantis Press, 2011. http://dx.doi.org/10.2991/eusflat.2011.56.

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Regensburger, Georg, Markus Rosenkranz, and Johannes Middeke. "A skew polynomial approach to integro-differential operators." In the 2009 international symposium. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1576702.1576742.

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Reports on the topic "Integro-Differential"

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Caraus, Lurie, and Zhilin Li. A Direct Method and Convergence Analysis for Some System of Singular Integro-Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, January 2003. http://dx.doi.org/10.21236/ada451436.

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