\(L\)-stable Simpson's 3/8 rule and Burgers' equation

DOI10.1016/j.amc.2011.06.017zbMath1229.65188OpenAlexW1976046473MaRDI QIDQ648327

Juan-Miguel Gracia

Publication date: 22 November 2011

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.06.017

zbMATH Keywords

numerical examplesdiffusion equationBurgers equationunconditional stability\(L\)-stabilityHopf-Cole transformationMathematica 7.0backward Euler formulaorigin 7.5Simpson's 3/8 rule

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Heat equation (35K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

On a weakly L‐stable time integration formula coupled with nonstandard finite difference scheme with application to nonlinear parabolic partial differential equations ⋮ \(L\)-stable derivative-free error-corrected trapezoidal rule for Burgers' equation with inconsistent initial and boundary conditions ⋮ Higher order time integration formula with application on Burgers’ equation

Uses Software

• Mathematica

Cites Work

• A numerical method based on Crank-Nicolson scheme for Burgers' equation
• A class of generalized trapezoidal formulas for the numerical integration of
• The Extrapolation of First Order Methods for Parabolic Partial Differential Equations. I
• Generalized trapezoidal formulas for parabolic equations
• A new L-stable Simpson-type rule for the diffusion equation
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics
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