A numerical scheme based on a solution of nonlinear advection--diffusion equations

DOI10.1016/j.cam.2004.02.019zbMath1107.65345OpenAlexW2064619682MaRDI QIDQ704173

Isao Kimura, Katsuhiro Sakai

Publication date: 13 January 2005

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

Full work available at URL: https://doi.org/10.1016/j.cam.2004.02.019

zbMATH Keywords

Cole-Hopf transformationSpectral methodNumerical stabilityHyperbolic equationNonlinear advection-diffusion equationNumerical oscillations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (5)

On the class of high order time stepping schemes based on Padé approximations for the numerical solution of Burgers' equation ⋮ Numerical Solution of Two-Dimensional Advection–Diffusion Equation Using Generalized Integral Representation Method ⋮ Fast boundary-domain integral method for unsteady convection-diffusion equation with variable diffusivity using the modified Helmholtz fundamental solution ⋮ Integral equation formulation of an unsteady diffusion-convection equation with variable coefficient and velocity ⋮ Multistep methods for the numerical simulation of two-dimensional Burgers' equation

Cites Work

• High resolution schemes for hyperbolic conservation laws
• A stable and accurate convective modelling procedure based on quadratic upstream interpolation
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• A numerical scheme for transport equations with spatially distributed coefficients based on locally exact difference method
• A nonoscillatory numerical scheme based on a general solution of 2-D unsteady advection-diffusion equations
• Hyperbolic systems of conservation laws II
• APPLICATION OF THE LOCALLY ANALYTIC DIFFERENCING SCHEME TO SOME TEST PROBLEMS FOR THE CONVECTION-DIFFUSION EQUATION
• Uniformly High-Order Accurate Nonoscillatory Schemes. I
• On a quasi-linear parabolic equation occurring in aerodynamics
• RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER

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