On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials

Solving singular integral equations by using orthogonal polynomials

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

NUMERICAL APPROACH TO SOLVE SINGULAR INTEGRAL EQUATIONS USING BPFS AND TAYLOR SERIES EXPANSION

In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given.

On the Volterra Integral Equation with Weakly Singular Kernel

Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel

In this paper, numerical solutions of the linear and nonlinear fractional integrodifferential equations with weakly singular kernel where fractional derivatives are considered in the Caputo sense, have been obtained by Legendre wavelets method. The block pulse functions and their properties are employed to derive a general procedure for forming the operational matrix of fractional integration f...

Fractional differential equations with Legendre polynomials