For one class of the singular integro-differential equations with Cauchy kernel on an interval, a Galerkin method is justified. The convergence is proved and the error estimation is given.

We consider the following partial integro-differential equation (Allen–Cahn equation with memory): φt = ∫ t 0 a(t − t ′)[ ∆φ + f (φ)+ h](t ′) dt ′, where is a small parameter, h a constant, f (φ) the negative derivative of a double well potential and the kernel a is a piecewise continuous, differentiable at the origin, scalar-valued function on (0,∞). The prototype kernels are exponentially dec...

The numerical stability of the polynomial spline collocation method for general Volterra integro-differential equation is being considered. The convergence and stability of the newmethod are given and the efficiency of the newmethod is illustrated by examples. We also proved the conjecture suggested by Danciu in 1997 on the stability of the polynomial spline collocation method for the higher-or...

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

A numerical scheme, based on the cubic B-spline wavelets for solving fractional integro-differential equations is presented. The fractional derivative of these wavelets are utilized to reduce the fractional integro-differential equation to system of algebraic equations. Numerical examples are provided to demonstrate the accuracy and efficiency and simplicity of the method.

Abstract. In this study we developed and modified Taylor expansion method for approximating the solution of linear Fredholm and Volterra integro-differential equations. Via Taylor’s expansion of the unknown function at an arbitrary point, the integro-differential equations to be solved is approximately transformed into a system of linear equations for the unknown and its derivatives which can b...

Nonlinear partial differential equations (NLPDEs) are widely utilized in engineering and physical research to represent many processes of naturalistic occurrences. In this paper, we investigate two well-known NLPDEs, namely, the (2 + 1)-dimensional first integro-differential KP hierarchy equation second equation, through a well-stable algorithm known as (G′G′+G+A)-expansion approach for time. T...

This article studies the development of two numerical techniques for solving convection-diffusion type partial integro-differential equation (PIDE) with a weakly singular kernel. Cubic trigonometric B-spline (CTBS) functions are used interpolation in both methods. The first method is CTBS based collocation which reduces PIDE to an algebraic tridiagonal system linear equations. other differentia...

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...