A variational form with Legendre series for linear integral equations

Abstract

In this work, we seek the approximate solution of integral equations by truncation Legendre series approximation using a variational form for the equation. this one is reduced to a linear system where the solution of this latter gives the Legendre coefficients and thereafter the solution of the equation.The convergence and the error analysis of this method are discussed. Finally, we compare our numerical results by others.

Solving linear integral equations with Fibonacci polynomial

“…The Taylor-series expansion method for a class of Volterra integral equations of second kind with smooth or weakly singular kernels where the authors transform integral equation to linear differential equation [5]. The application of the four Chebyshev polynomials, Legendre wavelets, Bernoulli series, Euler series, Legendre series and Hermite series with hat basis functions for solving linear integral equations [6][7][8][9][10][11][12].…”