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.
Highlights
IntroductionMany mathematical models of natural and applied sciences phenomena such as fluid mechanics, hydrodynamics, electromagnetics and various areas of physics are based on hyperbolic partial differential equations
Some results of this paper, without proof, are pre-Many mathematical models of natural and applied sciences phenomena such as fluid mechanics, hydrodynamics, electromagnetics and various areas of physics are based on hyperbolic partial differential equations
Nonlocal boundary condition is a relation between the values of unknown function on the boundary and inside of the given domain
Summary
Many mathematical models of natural and applied sciences phenomena such as fluid mechanics, hydrodynamics, electromagnetics and various areas of physics are based on hyperbolic partial differential equations. Modeling some of these sented in [27]. Boundary value problems with nonlocal boundary conditions have become a rapidly growing area of research. Such types of boundary conditions are encountered in applications including thermoelasticity [1], climate control systems [2] and financial mathematics [3]. 0, On stable high order difference schemes for hyperbolic problems with the Neumann boundary conditions 61 x ∈ S, S = S1 ∪ S2 are considered.
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