Analytical numerical method for solving nonlinear partial differential equations

A new technique for solving partial differential equations has been developed and tested. The technique uses step integration over a small interval of the independent variable after applying the finite difference for the partial derivatives. The integration is carried out for each element while using average values for the neighboring elements. These values are modified by iteration. The technique is used here for solving Burgers' equation. The results demonstrate excellent agreement with that of the exact solution.