An Iterative Finite-Difference Method for Hyperbolic Systems

Finite-Difference Methods for Nonlinear Hyperbolic Systems

is obtained where A (u) is the Jacobian matrix of the components of / with respect to the components of u. Equation (1.2) is said to be hyperbolic if the eigenvalues of the matrix pi + 6A are real for all real numbers m, 0. Several authors have proposed finite-difference schemes for the numerical integration of (1.1) (or (1.2)). In [6], Lax and Wendroff introduced an explicit scheme which is st...

On Certain Finite Difference Schemes For Hyperbolic Systems

Finite difference method for solving partial integro-differential equations

In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...

Discontinuous Hamiltonian Finite Element Method for Linear Hyperbolic Systems

We develop a Hamiltonian discontinuous finite element discretization of a generalized Hamiltonian system for linear hyperbolic systems, which include the rotating shallow water equations, the acoustic and Maxwell equations. These equations have a Hamiltonian structure with a bilinear Poisson bracket, and as a consequence the phase-space structure, “mass” and energy are preserved. We discretize ...

A Finite Element Method for First-Order Hyperbolic Systems

A new finite element method is proposed for the numerical solution of a class of initial-boundary value problems for first-order hyperbolic systems in one space dimension. An application of our procedure to a system modeling gas flow in a pipe is discussed. Asymptotic error estimates are derived in the L norm in space.