On stable high order difference schemes for hyperbolic problems with the Neumann boundary conditions

Abstract

In this paper, third and fourth order of accuracy stable difference schemes for approximately solving multipoint nonlocal boundary value problems for hyperbolic equations with the Neumann boundary conditions are considered. Stability estimates for the solutions of these difference schemes are presented. Finite difference method is used to obtain numerical solutions. Numerical results of errors and CPU times are presented and are analyzed.

Keywords

• Nonlocal and multipoint BVPs
• Stability
• Abstract hyperbolic equations
• Finite difference methods