A robust numerical method for solving time-dependent singularly perturbed two-parameter problem using nonstandard finite difference method

This paper presents a numerical scheme based on a nonstandard finite difference method for solving the singularly perturbed time-dependent two-parameter problem. This model is a common occurrence in the theory of chemical flow reactors and boundary layers controlled by fluid suction. There are several numerical methods in the literature for solving singularly perturbed two-parameter problems with temporal dependence, but most of them are either of low order or else dependent on parameter. Here, we have constructed a numerical method based on Crank–Nicolson in time and by nonstandard finite difference (NSFD) in space. Consequently, the derived method is found to be higher-order accurate in space and time and also shows parameter uniformity. An extensive convergence analysis has been performed to demonstrate the method’s uniform convergence and the numerical answers back up the theoretical findings of the study.