Fourth-order difference methods for hyperbolic IBVPs
This paper deals with explicit and implicit fourth-order difference approximations of initial-boundary value problems (IBVPs) for hyperbolic partial differential equations. The method of lines, energy estimations and the Laplace transform technique are used. A complete stability theory for the implicit fourth-order approximation is presented. The theoretical properties are verified through a number of numerical experiments. The results show that the fourth-order methods are more efficient than the standard second-order one.
explicit and implicit fourth-order difference approximations
scientific article; zbMATH DE number 758605