Numerical Solutions of the Burgers Equation: A Comparative Study of Finite Difference and Differential Quadrature Methods

The Finite Difference Method (FDM) and Differential Quadrature Method (DQM) are utilized to solve the partial differential equation in Burgers-Huxley equation. While FDM is relatively simple to implement, it tends to yield less accurate results. To address this limitation, DQM is employed, which improves accuracy but requires more computational effort and time. Various numbers of nodes are used in these methods to examine their accuracy. A program developed in C language based on these methods is used to solve Burgers’ equation. The results are compared in terms of numerical solution accuracy and convergence. Overall, the numerical results indicate that the Differential Quadrature Method outperforms the Finite Difference Method in both accuracy and convergence.