Results 221 to 230 of about 43,848 (263)

Integro-Differential Equations

1992
The aim of this chapter is to extend some results of Chapters 1 – 7 concerning boundedness, convergence and quasiconvergence to a class of integro-differential equations with retarded argument which arises from phase synchronization problems. Our aim is to apply ordinary differential equation methods such as the Bakaev-Guzh technique and non-local ...
Gennadij A. Leonov, Volker Reitmann, Vera B. Smirnova   +2 more
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Improvement by projection for integro‐differential equations

Mathematical Methods in the Applied Sciences, 2020
The aim of this work is to establish an improved convergence analysis via Kulkarni method to approximate the solution of an integro‐differential equation in . We prove the following convergence orders: Kulkarni order is , and Kulkarni iterated order is . The present study extends and improves earlier results in the literature.
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Integro-Differential Equations of Fractional Order

Differential Equations and Dynamical Systems, 2012
For a Cauchy type problem for a two-dimensional integro-differential equation of fractional order the global unique existence of a solution is proved if the nonlinearity satisfies a global Lipschitz condition with a sufficiently small Lipschitz constant.
Abbas, Saïd, Benchohra, Mouffak, Graef, John R.   +2 more
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Global nonexistence for an integro‐differential equation

Mathematical Methods in the Applied Sciences, 2011
The initial boundary value problem for an integro‐differential equation with nonlinear damping and source terms in a bounded domain is considered. By modifying the method in a work by Autuori et al. in 2010, we establish the nonexistence result of global solutions with the initial energy controlled by a critical value.
Wu, Shun-Tang, Lin, Ching-Yan
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On a System of Integro-Differential Equations

SIAM Journal on Applied Mathematics, 1971
In this paper a system of integro-differential equations arising in reactor dynamics is studied. To obtain existence theorems and some qualitative properties of the solution we use methods of functional analysis, specifically, the theory of strongly continuous semigroups of operators on a Banach space. In Appendix A, a lemma is proved about convergence
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Collocation Methods for Integro-Differential Equations

SIAM Journal on Numerical Analysis, 1977
In this note we extend the work of de Boor and Swartz (SIAM J. Numer. Anal., 10 (1973), pp. 582-606) on the solution of two-point boundary value problems by collocation. In particular, we are concerned with boundary value problems described by integro-differential equations involving derivatives of order up to and including m with m boundary conditions.
Hangelbroek, Rutger J., Kaper, Hans G., Leaf, Gary K.   +2 more
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Integro-Differential Equation

2015
Solving for the complete many-body wave function (instead of partial waves in a PH expansion), one gets an integro-differential equation (IDE). The IDE is derived from PH expansion method. Hence, IDE and PHEM are equivalent. Still IDE has certain advantages: its structure and complexity do not increase with the number of particles. Also, since there is
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On a Nonlinear Singular Integro‐Differential Equation

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1987
The author [ibid. 63, 249-259 (1983; Zbl 0525.45004) and 65, 309-310 (1985; Zbl 0573.45004)] applied methods of monotone operator theory to some classes of nonlinear singular integral and integrodifferential equations of Cauchy type. In particular, in the first cited paper, the main theorem of the theory of maximal monotone operators was used to prove ...
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Solving integral equations in free space with inverse-designed ultrathin optical metagratings

Nature Nanotechnology, 2023
Andrea Cordaro, Andrea Alu
exaly  

DeepXDE: A Deep Learning Library for Solving Differential Equations

SIAM Review, 2021
Lu Lu, George E Karniadakis
exaly