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...

The Lax-Wendro↵ time discretization is an alternative method to the popular total variation diminishing Runge-Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in general more compact and e cient than RKDG methods ...

In this paper, high order central finite difference schemes in a finite interval are analyzed for the diffusion equation. Boundary conditions of the initial-boundary value problem (IBVP) are treated by the simplified inverse Lax-Wendroff (SILW) procedure. For the fully discrete case, a third order explicit Runge-Kutta method is used as an example for the analysis. Stability is analyzed by both ...

The finite difference methods of Godunov, Hyman, Lax and Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, the artificial compression method of Harten, and Glimm’s method, a random choice method, are discussed. The methods are used to integrate the one-dimensional Eulerian form of the equations of gas d...

Harmonic wave excitation in a semi-infinite incompressible hyperelastic 1D rod with the Mooney–Rivlin equation of state reveals formation and propagation shock fronts arising between faster slower moving parts initially harmonic wave. The observed result collapse being absorbed by parts; hence, to attenuation kinetic elastic strain energy corresponding heat generation. Both geometrically physic...

Abstract We consider numerical boundary conditions for high order finite difference schemes for solving convection-diffusion equations on arbitrary geometry. The two main difficulties for numerical boundary conditions in such situations are: (1) the wide stencil of the high order finite difference operator requires special treatment for a few ghost points near the boundary; (2) the physical bou...