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