A Reliable Algorithm for solution of Higher Dimensional Nonlinear (1 + 1) and (2 + 1) Dimensional Volterra-Fredholm Integral Equations

An approach to approximate solution of higher dimensional Volterra-Fredholm integral equations (VFIE) is presented in this paper. A well-established semi analytical method is extended to solution of VFIE for the first time, called Optimal Homotopy Asymptotic Method (OHAM). The efficiency and effectiveness of the proposed technique is tested upon (1+ 1) and (2+ 1) dimensional VFIE. Results obtained through OHAM are compared with multi quadric radial basis function method,radial basis function method, modified block-plus function method, Bernoulli collocation method, efficient pseudo spectral scheme, three dimensional block-plus function methods and 3D triangular function. The comparison clearly shows the effectiveness and reliability of the presented technique over these methods. Moreover, the use of OHAM is simple and straight forward.