Boundary value problems for second order integro-differential equations of Fredholm type

“…In [8] [9], compact finite-differences for one-dimensional PIDEs are studied. Additional results on high-order schemes for integro differential equations (IDE) can be found in [10]. The research in [11], is devoted to an iterated Galerkin method for PIDE in one-dimesion; see [12].…”

Section: Introductionmentioning

confidence: 99%

Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator

Gathungu¹,

Borzì²

2017

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An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.

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“…For a comprehensive introduction about the existence and uniqueness theory of solution of such problems, we refer to [25,26]. Additionally, we assume that IDEs (1) and (2) have a unique solution ( ) under the above two assumptions on the given interval.…”

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confidence: 99%

Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

Komashynska

Al‐Smadi

2014

Journal of Applied Mathematics

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We present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments.

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Boundary value problems for second order integro-differential equations of Fredholm type

Cited by 18 publications

References 5 publications

Numerical solving initial value problem for Fredholm type linear integro-differential equation system

Numerical solving initial value problem for Fredholm type linear integro-differential equation system

Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator

Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

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