We develop a class of numerical methods for stiff systems, based on the method of exponential time differencing. We describe schemes with secondand higher-order accuracy, introduce new Runge–Kutta versions of these schemes, and extend the method to show how it may be applied to systems whose linear part is nondiagonal. We test the method against other common schemes, including integrating facto...

In this paper, we will present an effective simulation to study the solution behavior of a high dimensional chaos by considering nine-dimensionalLorenz system through Rabotnov fractional-exponential (RFE) kernel fractional derivative. First, derive approximate formula thefractional-order derivative polynomial function $t^{p}$ in terms RFE kernel. work, use spectral collocation method basedon pr...

In this paper, we present a study of some high-order compact difference schemes for solving the Fitzhugh-Nagumo equations governed by two coupled time-dependent nonlinear reaction diffusion equations in two variables. Solving the Fitzhugh-Nagumo equations is quite challenging, since the equations involve spatial and temporal dynamics in two different scales and the solutions exhibit shock-like ...

In this paper, a fractional order HIV/AIDS (FOHA) epidemic model with treatment is investigated. The first step in the proposed procedure is represent the FOHA system as an equivalent system of ordinary differential equations. In the second step, we solved the system obtained in the first step by using the well known fourth order Runge-Kutta method. Numerical simulations are also presented to v...

This paper is concerned with time-stepping numerical methods for computing stiff semi-discrete systems of ordinary differential equations for transient hypersonic flows with thermo-chemical nonequilibrium. The stiffness of the equations is mainly caused by the viscous flux terms across the boundary layers and by the source terms modeling finite-rate thermo-chemical processes. Implicit methods a...

We propose a class of semi-Lagrangian methods of high approximation order in space and time, based on spectral element space discretizations and exponential integrators of Runge-Kutta type. The methods were presented in [7] for simpler convection-diffusion equations. We discuss the extension of these methods to the Navier-Stokes equations, and their implementation using projections. SemiLagrang...

The objective of this study was to develop a computer simulation algorithm to dynamically estimate and predict the growth of Clostridium perfringens in cooked ground beef. The computational algorithm was based on the implicit form of the Gompertz model, the growth kinetics of C. perfringens in cooked ground beef, and the fourth-order Runge-Kutta numerical method. This algorithm was validated us...

In this paper, numerical spline-based differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. For the time integration of the problem, the Runge–Kutta and spline-based differential quadrature methods have been applied. The Runge–Kutta method was unstable for solving the prob...