Solving 2D-Poisson equation using modified cubic B-spline differential quadrature method

In this study a modified cubic B-spline differential quadrature method (MCBDQM) is used to solve the two dimensional Poisson equation. Using the cubic B-spline functions, explicit expressions of weighting coefficients for approximation of derivatives are obtained. Examples of two dimensional Poisson equation under Dirichlet and mixed boundary conditions are studied using the method. Comparisons between the results of the method, the results of using Shu's general approach and results of other methods are presented. Good agreement with Shu's general approach and with the other methods is reached in case of Dirichlet boundary condition. The differential quadrature based on modified cubic B-splines is found to be an efficient method to solve the two dimensional Poisson equation. Keywords: Differential quadrature method, Modified cubic B-spline, Shu’s general approach, Two dimensional Poisson equatio