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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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
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Abstract	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.
AbstractList	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.
Author	Karaguler, Turhan Sinsoysal, Bahaddin Rasulov, Mahir
Author_xml	– sequence: 1 givenname: Mahir surname: Rasulov fullname: Rasulov, Mahir email: mresulov@beykent.edu.tr organization: Department of Mathematics and Computing, Beykent University, Buyukcekmece, Istanbul 34900, Turkey – sequence: 2 givenname: Turhan surname: Karaguler fullname: Karaguler, Turhan organization: Department of Mathematics and Computing, Beykent University, Buyukcekmece, Istanbul 34900, Turkey – sequence: 3 givenname: Bahaddin surname: Sinsoysal fullname: Sinsoysal, Bahaddin email: bahattin@risc01.ktu.edu.tr organization: Department of Mathematics, Karadeniz Technical University, Trabzon 61080, Turkey
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Keywords	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
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SubjectTerms	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
Title	Finite difference method for solving boundary initial value problem of a system hyperbolic equations in a class of discontinuous functions
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