Smoothing of Crank–Nicolson scheme for the two-dimensional diffusion with an integral condition

The Parabolic partial differential equations (PDEs) with nonlocal boundary conditions model various physical phenomena, e.g. chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. This paper deals with the smoothing of the Crank–Nicolson numerical scheme for two-dimensional parabolic PDEs with nonlocal boundary conditions. We use the numerical scheme based on Padé approximations of the matrix exponential. The graphs of numerical results demonstrate the successful smoothing of the Crank–Nicolson numerical scheme.