Stability analysis of finite difference schemes for two-dimensional hyperbolic equations using Fourier transforms

Authors:

Dadabayev Sardor Usmanovich,Mirzaahmedov Muhammadbobur Karimberdiyevich,

DOI NO:

https://doi.org/10.26782/jmcms.2019.04.00017

Keywords:

Hyperbolic equation,fourier transform,difference schemes, stability analysis ,

Abstract

In a lot of papers the main focus is given to study finite difference schemes for one dimensional hyperbolic equation. Since this idea is valid for one dimensional hyperbolic equation, one can also consider finite difference schemes for two dimensional hyperbolic equations. It is convenient to apply Fourier transform to check stability analysis. The present paper studies stability analysis of finite difference schemes for two dimensional hyperbolic equations with constant coefficients [IV].

Refference:

I.A.M.Blokhin, R.D. Aloev “Energy integrals and thier applications to investigation of stability of difference schemes”. Novosibirsk, 1993. 224 p.

II.A.G.Kulikovskii, N.V.Pogorelov,A.Yu.Semenov “Mathematical problems of numerical solution of hyperbolic systems”. M.:Physics and mathematics publishers, 2001, 608 p.

III.A.M.Blokhin,I.G.Sokovikov “About one approach to formulation of difference schemes for quasi-linear equations of gas dynamics”. Siberian Mathematical Journal, 1999, V.40, No 6, Pp.1236-1243.

IV.A.Harten “On the symmetric form of systems of conservation laws with enthropy”. J. Comput. Phys. 1983. V. 49, No 1, p.151-164.

V.A. M. Blokhin and R. D. Aloev, “Energy Integrals and Their Applications to Investigation of Stability of Difference Schemes”, Novosibirsk, 1993. 224 p(in Russian).

VI.A. I. Vol’pert and S. I. Khudyaev, “On the Cauchy problem for composite systems of nonlinear differential equations”,Math. USSR Sb.,16 (1972), 517–544.

VII.R. D. Aloev, Z. K. Eshkuvatov, Sh. O. Davlatov and N. M. A. Nik Long, “Sufficient condition of stability of finite element method for symmetric t-hyperbolic systems with constant coefficients”,Computersand Mathematics with Applications,68 (2014), 1194–1204.

VIII.R. D. Aloev,A. M. Blokhin and M. U. Hudayberganov, “One class of stable difference schemes for hyperbolic system”, American Journal of Numerical Analysis,2(2014), 85–89.

IX.S. K. Godunov, “Equations of Mathematical Physics”, Nauka, Moscow, 1979 (in Russian).

X.S. K. Godunov, “An interesting class of quasi-linear systems”, Dokl. Akad. Nauk SSSR,139 (1961), 521–523. (in Russian).

Dadabayev Sardor Usmanovich , Mirzaahmedov Muhammadbobur Karimberdiyevich View Download