Lerch matrix collocation method for 2D and 3D Volterra type integral and second order partial integro differential equations together with an alternative error analysis and convergence criterion based on residual functions

Abstract

In this study, second order linear Volterra partial integro-differential equation with two- and three-dimensional are solved by collocation method based on Lerch polynomials. This method is composed of the operational matrix and collocation methods, which are based upon the matrix forms of the Lerch polynomials with the parameter ? and Taylor polynomials, and their derivatives and integrals. The approximate solutions of the mentioned equations are investigated in terms of the Lerch polynomials the different values of ?. Also, to verify the accuracy and efficiency of the present method, an alternative convergence criterion along with error analysis depending on residual function is enhanced. Moreover, the obtained numerical results are compared with other methods and scrutinized by using tables and figures. © TÜBİTAK