A Meshless collocation method for the approximate solution of a partial integro-differential equation

Abstract

In this paper, a radial basis functions based collocation technique is developed to approximate solution of a partial integrodifferential equation having a weakly singular kernel. The time derivative is approximated using backward finite difference approach while radial basis functions are collocated of over the spatial domain. Two types of radial basis functions namely Multiquadric and quantic are employed. Accuracy of the proposed method is evaluated in terms of ܮଶ and ܮஶ , and by taking various time step sizes and different number of collocation points in the spatial domain. Numerical results of four test problems from literature are provided to study the accuracy and applicability of this method. Sufficient simulations are done to validate the method. Comparison of the results is also made with an existing method from literature.