The comparison of the stability of the Adomian decomposition method with numerical methods of equation solution

DOI10.1016/j.amc.2006.08.011zbMath1114.65077OpenAlexW2018040930MaRDI QIDQ876646

N. E. Zubov

Publication date: 26 April 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.08.011

zbMATH Keywords

stabilityconvergencecollocation methodcomparison of methodsintegral equationnumerical examplesfinite difference schemeRunge-Kutta methodTaylor series methodinitial value and boundary value problems

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Volterra integral equations (45D05) Linear boundary value problems for ordinary differential equations (34B05)

Related Items

Laplace transform‐based approximation methods for solving pure aggregation and breakage equations ⋮ Improved finite difference technique via Adomian polynomial to solve the coupled Drinfeld's-Sokolov-Wilson system ⋮ Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions ⋮ Unnamed Item ⋮ A novel optimized decomposition method for Smoluchowski's aggregation equation

Cites Work

• A comparison between Adomian decomposition method and Taylor series method in the series solutions
• Solving frontier problems of physics: the decomposition method
• Variational approach to the sixth-order boundary value problems
• The existence of noise terms for systems of inhomogeneous differential and integral equations
• The Adomian decomposition method for fuzzy system of linear equations
• Restarted Adomian method for integral equations
• Analytic treatment for variable coefficient fourth-order parabolic partial differential equations
• Application of the Adomian decomposition method for two-dimensional parabolic equation subject to nonstandard boundary specifications
• Convergence of Adomian's Method
• The numerical solution of fifth-order boundary value problems by the decomposition method