Numerical solution of Burgers equation by the Sobolev gradient method

DOI10.1016/j.amc.2011.08.005zbMath1415.65241OpenAlexW2025054824MaRDI QIDQ426932

Sultan Sial, Nauman Raza, John W. Neuberger

Publication date: 13 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.08.005

zbMATH Keywords

Burgers equationvariational methodSobolev gradientsteepest descentmodified Adomian method

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (5)

Numerical solution of Burgers' equation by cubic Hermite collocation method ⋮ A link between the steepest descent method and fixed-point iterations ⋮ Numerical solutions of singularly perturbed reaction diffusion equation with Sobolev gradients ⋮ Sobolev gradient preconditioning for elliptic reaction-diffusion problems with some nonsmooth nonlinearities ⋮ Polynomial solution of singular differential equations using Weighted Sobolev gradients

Cites Work

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• Approximate solutions to Poisson-Boltzmann systems with Sobolev gradients
• Preconditioning operators and Sobolev gradients for nonlinear elliptic problems
• Sobolev gradient preconditioning for the electrostatic potential equation
• Approximating time evolution related to Ginzburg-Landau functionals via Sobolev gradient methods in a finite-element setting
• Application of Sobolev gradient method to Poisson-Boltzmann system
• Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionals
• Energy minimization related to the nonlinear Schrödinger equation
• The group explicit method for the solution of Burger's equation
• Energy minimization using Sobolev gradients: application to phase separation and ordering.
• A numerical solution of Burgers' equation by modified Adomian method
• A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates
• A numerical solution of Burgers' equation
• A direct variational method applied to Burgers' equation
• Sobolev preconditioning for the Poisson-Boltzmann equation
• Constructing fair curves and surfaces with a Sobolev gradient method
• A variational approach to an elastic inverse problem
• Sobolev gradient preconditioning for image‐processing PDEs
• Equivalent Norms for Sobolev Spaces
• The partial differential equation u_t + uu_x = μ_xx
• On a quasi-linear parabolic equation occurring in aerodynamics

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