A Galerkin solution to a regularized Cauchy singular integro-differential equation

Justification of a Galerkin Method for a Regularized Cauchy Singular Integro-differential Equation

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.

Numerical Solution of Singular Integro-differential Equations with Cauchy Kernel

The main purpose of this article is to present an approximation method of for singular integrodifferential equations with Cauchy kernel in the most general form under the mixed conditions in terms of the second kind Chebyshev polynomials. This method transforms mixed singular integro-differential equations with Cauchy kernel and the given conditions into matrix equation and using the zeroes of ...

Numerical solution of the Fredholm singular integro-differential equation with Cauchy kernel by using Taylor-series expansion and Galerkin method

In this paper, we present a Taylor-series expansion method for a class of Fredholm singular integro-differential equation with Cauchy kernel. This method uses the truncated Taylor-series polynomial of the unknown function and transforms the integro-differential equation into an nth order linear ordinary differential equa.tion with variable coefficients: ~y Galerkin method we use the orthogonal ...

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 ...

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