A COMPUTATIONAL ALGORITHM FOR THE SOLUTION OF SECOND ORDER PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH A WEAKLY SINGULAR KERNEL USING QUINTIC B-SPLINE COLLOCATION METHOD

S. AHMAD, A. ALI, S. I. A. SHAH, FAZAL-I- HAQ

Abstract


A quintic B-spline collocation method is considered for numerical solution of partial integro-differential equations with a weakly singular kernel. To discretize the time derivative a backward difference formula is employed while the spatial derivatives are approximated via quintic B-spline functions. Approximate solution of a test problem is provided to validate the scheme. Accuracy of the method is assessed in terms of 𝐿𝐿∞ and 𝐿𝐿2 error norms. Better accuracy is obtained and the results are compared with Quasi-wavelet method.

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