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L. D. Ropp, N. J. Shadid and C. C. Ober, “Studies of the Accuracy of Time Integration Methods for Reaction-Diffusion Equations,” Journal of Computational Physics, Vol. 194, No. 2, 2004, pp. 544-574. http://dx.doi.org/10.1016/j.jcp.2003.08.033

has been cited by the following article:

• TITLE: An Efficient Method to Solve Thermal Wave Equation

  AUTHORS: Mohamed Salah, R. M. Amer, M. S. Matbuly

  KEYWORDS: Reaction-Diffusion; Block Marching; Differential Quadrature; Perturbation

  JOURNAL NAME: Applied Mathematics, Vol.5 No.3, February 13, 2014

  ABSTRACT: In this paper, an efficient technique of differential quadrature method and perturbation method is employed to analyze reaction-diffusion problems. An efficient method is presented to solve thermal wave propagation model in one and two dimensions. The proposed method marches in the time direction block by block and there are several time levels in each block. The global method of differential quadrature is applied in each block to discretize both the spatial and temporal derivatives. Furthermore, the proposed method is validated by comparing the obtained results with the available analytical ones and also compared with the hybrid technique of differential quadrature method and Runge-Kutta fourth order method.