Dimension reduction analysis with mapping and direct integration algorithm

Based on the Lagrange series interpolation, the semi-analytical and direct integration method (DIM) for solving the multi-dimensional partial differential equations are presented in this paper. A multidimensional problem can be simplified to a set of the ordinary differential equation by the mapping technique and Lagrange series interpolation (dimension reduction). The semi-analytical and numerical solutions by DIM are derived for the partial differential equation with variable coefficients. Comparisons with analytical solutions are performed in order to demonstrate the accuracy and efficiency of the proposed method.