Mathematical Model of Complete Shallow Water Problem with Source Terms, Stability Analysis of Lax-Wendroff Scheme

On the Stability of Friedrichs' Scheme and the Modified Lax-Wendroff Scheme*

Necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme with smooth coefficients are derived by means of Kreiss' Matrix Theorem and the first Stability Theorem of Lax and Nirenberg. In this note we derive necessary and sufficient stability criteria for Friedrichs' scheme and the modified Lax-Wendroff scheme [8] for the hyperbolic system n (1) ". =...

Existence of Discrete Shock Profiles for the Lax-wendroff Scheme

The Near - Stability of the Lax - Wendroff Method

In discussing finite difference methods for the solution of hyperbolic par t ia l differential equations, STETrER [1] used est imates on some absolutely convergent Fourier series to prove stabi l i ty and instabi l i ty with respect to uniform convergence. I f / , a complex valued function on the circle, has an absolutely convergent Fourier series, then the n-th power of ] also has an absolutel...

A gas-kinetic scheme for shallow–water equations with source terms

In this paper, the Kinetic Flux Vector Splitting (KFVS) scheme is extended to solving the shallow water equations with source terms. To develop a well-balanced scheme between the source term and the flow convection, the source term effect is accounted in the flux evaluation across cell interfaces. This leads to a modified gas–kinetic scheme with particular application to the shallow water equat...

Stability Analysis of Mathematical Model of Virus Therapy for Cancer

In this paper, we have analyzed a mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equations. We gain some conditions for global stability of trivial and interior equilibrium point.