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This article describes a numerical method based on the dual reciprocityboundary elements method (DRBEM) for solving some well-known nonlinearparabolic partial differential equations (PDEs). The equations include theclassic and generalized Fisher's equations, Allen-Cahn equation,Newell-Whithead equation, Fitz-HughNagumo equation and generalizedFitz-HughNagumo equation with time-dependent coefficients. The concept of thedual reciprocity is used to convert the domain integral to the boundary thatleads to an integration free method. We employ the time stepping scheme toapproximate the time derivative, and the linear radial basis functions (RBFs)are used as approximate functions in presented method. The nonlinear terms aretreated iteratively within each time step. The developed formulation isverified in some numerical test examples. The results of numerical experimentsare compared with analytical solution to confirm the accuracy and efficiency ofthe presented scheme.

The dual reciprocity boundary elements method for one-dimensional nonlinear parabolic partial differential equations