Split operator methods for hyperbolic systems in $p$ space variables

Split Operator Methods for Hyperbolic Systems in p Space Variables

(2) [/ 4§(/ rB)Ay\UY+i = [7 4W + rA)Ax]Um, [I+ÜIrA)Ax]Um+i = [I + hil + rB)Ay]U%li, where Um, Um+i are the values of U at the mesh points iih, jh, mk) and iih, jh, im + l)k) respectively, I is the unit matrix of order n, and r = k/h, where h, k are the mesh increments in the space and time directions respectively. The quantity Um+i is an auxiliary solution and in general is not an approximation...

Evolution Galerkin methods for hyperbolic systems in two space dimensions

The subject of the paper is the analysis of three new evolution Galerkin schemes for a system of hyperbolic equations, and particularly for the wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The main idea of the evolution Galerkin methods is the following: the initial function is evolved us...

Numerical methods for hyperbolic systems

Extended Monotone Methods for Hyperbolic Problems in Three Variables

We consider Initial-Boundary value problems associated with nonlinear hyperbolic partial differential equation in three independent variables, in a general setting wherein the forcing function is a sum of two monotonic functions. Employing natural lower-upper and coupled lower-upper solutions, we develop iterative schemes which converge uniformly and monotonically to the minimal-maximal and cou...

Operator-Based Preconditioning of Stiff Hyperbolic Systems

We introduce an operator-based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of PDEs posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a characteristic decomposition of the resulting directional parts. This approach allows for the solution of any number of characteristic components, f...