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

A. ALI, FAZAL-I- HAQ, S. AHMAD, Q. JAVAID

Abstract


A collocation method using septic B-spline functions is presented for approximate solution of a fourth order partial integro differential 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 via􀜮􀮶 and 􀜮􀬶 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.

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