A new approach to the nonlinear advection problem: An application of the decomposition method
type: Item
instance of: scholarly article
title: A new approach to the nonlinear advection problem: An application of the decomposition method
zbMATH Open document ID: 0838.65092
DOI: 10.1016/0096-3003(94)00182-4
author: Abdul-Majid Wazwaz
published in: Applied Mathematics and Computation
publication date: 1996-06-03T00:00:00Z
review text: The author uses the decomposition method of Adomian for solving the nonlinear parabolic (advection) equation \[ {\partial u \over \partial t} + u {\partial u \over \partial x} = f(x,t) \quad \text{with initial condition} \quad u(x,0) = g(x). \] The solution is obtained as a (truncated) series by calculating Adomian polynomials. Reviewer's remark: The author does not know recent works by K. Abbaoui and Y. Cherruault for estimating the accuracy of the method and for calculating easily (formal calculus) Adomian polynomials associated to any nonlinear operator.
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 839108
zbMATH Keywords: nonlinear parabolic (advection) equation
zbMATH Keywords: decomposition method
zbMATH Keywords: Adomian polynomials
reviewed by: Yves Cherruault
MaRDI profile type: Publication
full work available at URL: 0096-3003(94)00182-4
OpenAlex ID: W1985073491
cites work: A Fourier series method for the numerical solution of a class of parabolic partial differential equations
cites work: A Fourier series method for the numerical solution of the nonlinear advection problem
cites work: Solving frontier problems of physics: the decomposition method
cites work: Nonlinear equations with mixed derivatives
cites work: A new approach to nonlinear partial differential equations
cites work: Noise terms in decomposition solution series
description: scientific article; zbMATH DE number 839108