Numerical Solution of Singular Fredholm IntegroDifferential Equations of the Second Kind via PetrovGalerkin Method by using Legendre Multiwavelet

It is of interest to know whether we can solve a singular Fredholm integro-differential equation of the second kind with an infinite or semi-infinite range of integrate via Petrov–Galerkin method by using Legendre multiwavelet. For this purpose, we directly deal with infinite range of integrate. We introduce some change of variables for mapping infinite interval into a finite interval. After that, we use Petrov–Galerkin method with Legendre multiwavelet basis that yields linear system. Numerical results of our example will demonstrate accuracy and efficiency of the proposed method.