For solving first-order linear and nonlinear differential equations, a new two-stage implicit–explicit approach is given. The scheme’s first stage, or predictor implicit, while the second stage explicit. of proposed scheme an extended form existing Runge–Kutta scheme. stability consistency are also offered. In two phases, technique achieves third-order accuracy. method applied to SEIR epidemic ...

In this study, we obtain a numerical solution for Fisher's equation using experiment with three different cases. The cases correspond to coefficients the reaction term. We use methods namely; Forward-Time Central Space (FTCS) scheme, Nonstandard Finite Difference (NSFD) and Explicit Exponential (EEFD) scheme. first study properties of schemes such as positivity, boundedness, stability convergen...

systems in which reaction terms are coupled to diffusion and advection transports arise in awide range of chemical engineering applications, physics, biology and environmental. in these cases, thecomponents of the unknown can denote concentrations or population sizes which represent quantities andthey need to remain positive. classical finite difference schemes may produce numerical drawbacks s...

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...