Stability and Monotonicity of Difference Schemes for Nonlinear Scalar Conservation Laws and Multidimensional Quasi-linear Parabolic Equations

DOI10.2478/cmam-2009-0016zbMath1189.65209OpenAlexW1500210764MaRDI QIDQ3407848

S. V. Lemeshevskij, Piotr P. Matus

Publication date: 24 February 2010

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://elib.bsu.by/handle/123456789/42275

zbMATH Keywords

monotonicitystabilityBurgers equationRiemann problemscalar conservation lawsquasi-linear parabolic equationsdiscrete Bihari-type inequalitynonlinear finite-difference schemes

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Quasilinear parabolic equations (35K59)

Related Items

Analysis of second order difference schemes on non-uniform grids for quasilinear parabolic equations, A hybrid Godunov method for radiation hydrodynamics, Stability with respect to the initial data and monotonicity of an implicit difference scheme for a homogeneous porous medium equation with a quadratic nonlinearity, Globally stable difference schemes for the Fisher equation, Stability with respect to the input data and monotonicity of an implicit finite-difference scheme for a quasilinear parabolic equation, On the role of conservation laws in the problem on the occurrence of unstable solutions for quasilinear parabolic equations and their approximations, Stability and monotonicity of a conservative difference scheme for a multidimensional nonlinear scalar conservation law, Criterion for the stability of difference schemes for nonlinear differential equations, Numerical methods for a one-dimensional non-linear Biot's model, Компактные и монотонные разностные схемы для параболических уравнений, Compact and monotone difference schemes for the generalized Fisher equation