A COMPUTATIONAL TECHNIQUE FOR THE SOLUTION OF PARABOLIC TYPE INTEGRO-DIFFERENTIAL EQUATION WITH A WEAKLY SINGULAR KERNEL

A. ALI, S. AHMAD, S. I. A. SHAH, F. I. HAQ

Abstract


A quartic B-spline collocation method is proposed for numerical solution of partial integro-differential equations with a weakly singular kernel. The scheme is developed by discretization of the time derivative using forward difference formula while the spatial derivative is approximated using quartic B-spline functions. Numerical solution of two test problems are provided to validate the scheme. Accuracy of the method is assessed in terms of 􀜮∞ and 􀜮􀬶 error norms. Better accuracy is obtained and the results are also compared with cubic B-spline collocation method.

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