Abstract
The main objective of this work is to develop an efficient technique for solving bivariate linear or nonlinear Volterra integral equations. The method is based upon the cardinal spline functions on small compact supports. We express the known and unknown functions as linear combinations of translations of the spline functions. The integral equation is reduced to a system of algebra equations. Since the coefficient matrix for the algebraic system is nearly triangular. It is relatively straightforward to solve for the unknowns and an approximation of the original solution with high precision is achieved. Comparisons are made between our schemes and other techniques proposed in recent papers, and the improvement of our method is demonstrated with several numerical examples.