An efficient kernel-based method for solving nonlinear generalized Benjamin-Bona-Mahony-Burgers equation in irregular domains

Abstract

An iterative kernel-based method is proposed for solving the nonlinear generalized Benjamin-Bona-Mahony-Burgers equation in regular and irregular domains. The method is based on the positive definite kernels pseudospectral method. We have used an iterative linearization scheme to overcome the nonlinearity of the problem. The convergence of the linearization scheme is proved. The space-time kernels are used for the full discretization of the problems in the temporal and spatial domains. Here, we construct the multidimensional kernels using the product of one-dimensional kernels. Numerical results and comparisons are presented for the several two and three-dimensional problems with the various domains. The obtained results confirm the efficiency and accuracy of the proposed method.