Abstract
In this paper, we propose a meshless method using radial basis functions (RBFs) method based on finite-difference method to solve a nonlinear inverse convection–reaction–diffusion problem with an unknown source function. Indeed, the aim of this paper is to show that the meshless method based on the radial basis functions approach is also suitable for the treatment of the inverse nonlinear partial differential equations. Usually, the matrices obtained from the discretization of the equations are ill-conditioned, especially in higher-dimensional problems. To overcome such difficulties, we use Tikhonov regularization method. We prove that the time discrete scheme is stable using the energy method. The effectiveness of the proposed method is illustrated by numerical examples.
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