Finite difference method for solving boundary initial value problem of a system hyperbolic equations in a class of discontinuous functions

In this paper, a finite-difference method for solving boundary initial value problem of nonlinear system equations of hyperbolic type in a class of discontinuous functions is suggested. In order to obtain the numerical solution of the main problem in a class of discontinuous functions the auxiliary...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 149; no. 1; pp. 47 - 63
Main Authors: Rasulov, Mahir, Karaguler, Turhan, Sinsoysal, Bahaddin
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 05.02.2004
Elsevier
Subjects:
Computational hydrodynamics
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical modelling
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Shock waves
Shock waves
Numerical modelling
Computational hydrodynamics
Hyperbolic system
Initial value problem
Nonlinear problems
Non linear system
Algorithm
Partial differential equation
Equation system
Discontinuous equation
Non linear equation
Numerical analysis
Boundary value problem
Algorithm performance
Applied mathematics
Numerical solution
Hyperbolic equation
Problem solving
Finite difference method
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:In this paper, a finite-difference method for solving boundary initial value problem of nonlinear system equations of hyperbolic type in a class of discontinuous functions is suggested. In order to obtain the numerical solution of the main problem in a class of discontinuous functions the auxiliary problem is introduced. The degree of smoothness of the solution of the auxiliary problem is higher than of smoothness of the solution of the main problem. Furthermore, the suggested auxiliary problem lets us write out effective and higher order numerical algorithms. The solutions obtained from these algorithms represent the physical nature of the problem with a high accuracy. Some numerical experiments are carried out by using the auxiliary problem.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(02)00956-6