A computational method for fourth order partial integro-differential equation usingseptic B-spline

Abstract

A collocation method using septic B-spline functions is presented for approximate solution of a fourth order partialintegrodifferential equation with a weakly singular kernel. The second order time derivative is descritized by backward difference formula whereas the fourth order spatial derivativeis approximated usingseptic B-spline functions. The scheme is tested through a benchmark problem. Accuracy of the present scheme is assessed viaܮஶ and ܮଶ error norms. The scheme is examined using different number of collocation points, time step sizes and time levels. Comparison with quintic B-splinecollocation method is also made to validate the proposed method.