Derivation of the Adomian decomposition method using the homotopy analysis method

• Published in: Applied mathematics and computation Vol. 190; no. 1; pp. 6 - 14
• Main Author: Allan, Fathi M.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.07.2007; Elsevier
• Subjects: Adomian decomposition method; Convergence criteria; Error analysis; Exact sciences and technology; Homotopy analysis method; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, boundary value problems; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Convergence criteria; Error analysis; Adomian decomposition method; Homotopy analysis method; Initial value problem; Decomposition method; Mathematical method; Nonlinear problems; Partial differential equation; Convergence; Numerical analysis; Boundary value problem; Applied mathematics; Homotopy
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.12.074

Adomian decomposition method has been used intensively to solve nonlinear boundary and initial value problems. It has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits. However, very little has been done to address the mathematical foundation of the method and its error analysis. In this article the mathematical derivation of the method using the homotopy analysis method is presented. In addition, an error analysis is addressed as well as the convergence criteria.