The goal of this work is to develop an accurate numerical method which employs symbolic computation for solving linear and nonlinear multivariable integral and integro-differential equations of mathematical physics. When possible, a posteriori (and a priori) error estimates are sought to evaluate the effectiveness and accuracy of the projection methods used for obtaining the numeric solution. Projection methods such as collocation using different sets of basis functions on either a global or local basis are developed to obtain accurate and results. Symbolic computation permits previously insurmountable analytic manipulations to be performed for purposes of (1) developing expansion based solution methods, and (2) establishing error estimates and convergence rates. The major contribution of the investigation are twofold; (1) to exploit the development of symbolic manipulation for augmenting analytic, numeric, and graphic computation in support of solving and analyzing nonlinear integral and integro-differential equations of mathematical physics, and (2) to investigate, extend, and develop the recent formulation of Kumar and Sloan for scientific computation of multivariable equations.
