Singular perturbations of integro-differential equations

The Legendre Wavelet Method for Solving Singular Integro-differential Equations

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...

A Method to Estimate the Solution of a Weakly Singular Non-linear Integro-differential Equations by Applying the Homotopy Methods

Application of Tau Approach for Solving Integro-Differential Equations with a Weakly Singular Kernel

In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The  Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices....

Finite difference method for solving partial integro-differential equations

In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...

A Compact Scheme for a Partial Integro-Differential Equation with Weakly Singular Kernel

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...