×

The error estimates of generalized difference methods for 2nd order hyperbolic equations. (Chinese. English summary) Zbl 0656.65094

Hyperbolic equations are important in many physical and engineering studies, such as the wave equation. The solution of a hyperbolic equation is often a mixed initial-boundary value problem. Numerical solution from difference equation approximation is the most practical way of solving hyperbolic equations. The most important issues in numerical solution are error estimates and the convergence problem.
This paper discusses error estimates of generalized difference methods for second order hyperbolic equations under an abstract frame. Under this frame, the applications of Bellman’s inequality and norms defined in Hilbert space are used to obtain the optimal error estimates for semidiscrete and fully discrete states. Several examples are given in the paper to illustrate the practical applications of the optimal error estimates obtained under this abstract frame. Examples given include the 2-dimensional second-order elliptic operator and one-dimensional 4th- order elliptic operator as well.
Reviewer: Wu Minyen

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
PDFBibTeX XMLCite