This paper is concerned with time-stepping numerical methods for computing sti semi-discrete systems of ordinary di erential equations for transient hypersonic ows with thermo-chemical nonequilibrium. The sti ness of the equations is mainly caused by the viscous ux terms across the boundary layers and by the source terms modeling nite-rate thermo-chemical processes. Implicit methods are needed ...

1 Abstract. This paper examines a class of explicit nite-diierence advection schemes derived along the method of lines. An important application eld is large-scale atmospheric transport. The paper therefore focuses on the demand of positivity. For the spatial discretization, attention is connned to conservative schemes using 5 points per direction. The 4-th order central scheme and the family o...

Galerkin fully discrete approximations for parabolic equations with time-dependent coefficients are analyzed. The schemes are based on implicit Runge-Kutta methods, and are coupled with preconditioned iterative methods to approximately solve the resulting systems of linear equations. It is shown that for certain classes of Runge-Kutta methods, the fully discrete equations exhibit parallel featu...

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method an...

mhd boundary layer flow of two phase model nanofluid over a vertical plate is investigated both analytically and numerically. a system of governing nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations by suitable similarity transformations and then solved analytically using homotopy analysis method and numerically by the fourth order rung...

The Runge–Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservation laws is a high order finite element method, which utilizes the useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers, TVD Runge–Kutta time discretizations, and limiters. In this paper, we investigate using the RKDG finite element method for compressible...

this paper presents approximate analytical solutions for nonlinear oscillators using the multi-step homotopy analysis method (msham). the proposed scheme is only a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. several illustrat...

Generalized Fitzhugh– Nagumo equation; Polynomial differential quadrature method; Numerical solutions; Runge–Kutta method Abstract In this paper, polynomial differential quadrature method (PDQM) is applied to find the numerical solution of the generalized Fitzhugh–Nagumo equation with time-dependent coefficients in one dimensional space. The PDQM reduces the problem into a system of first order...

We study the linear stability of the fifth-order Weighted Essentially Non-Oscillatory spatial discretization (WENO5) combined with explicit time stepping applied to the one-dimensional advection equation. We show that it is not necessary for the stability domain of the time integrator to include a part of the imaginary axis. In particular, we show that the combination of WENO5 with either the f...