Computational analysis of some partial differential equations using efficient compact finite difference method.

In this article, the nonlinear partial differential equations are solved using compact finite difference method (CFDM6) of the sixth order accuracy. The mathematical models considered for the implementation of the proposed method are Burgers equation, Burgers-Fisher equation, modified Burgers equation and Burgers-Huxley equation. The execution of the method deals the spatial domain with CFDM6 and time integration with SSP-RK43. The efficacy of CFDM6 accentuates on the stability, which is handled using matrix stability analysis. To certify the accuracy and effectiveness of the proposed method, the results obtained for various test problems are compared with analytical solutions in literature. The L₂ and L_∞ error norms are calculated for test problems showing the efficacy of the method. The novelty of the article is observed with the sharp solution profile obtained in less computational time. [ABSTRACT FROM AUTHOR]