A two-step Adomian decomposition method

• Published in: Applied mathematics and computation Vol. 170; no. 1; pp. 570 - 583
• Main Author: Luo, Xing-Guo
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.11.2005; Elsevier
• Subjects: Adomian decomposition method; Difference and functional equations, recurrence relations; Exact sciences and technology; Finite differences and functional equations; Integral equations; Mathematical analysis; Mathematics; Nonlinear differential and integral equations; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Sciences and techniques of general use; Two-step; Nonlinear differential and integral equations; Adomian decomposition method; Two-step; Transcendental equation; Differential equation; Recurrence relation; Nonlinear differential equations; Functional equation; Step method; Difference equation; Non linear equation; Two step method; Numerical analysis; Applied mathematics; Integral equation; Two- step
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2004.12.010

The Adomian decomposition method (ADM) is a nonnumerical method for solving a wide variety of functional equations and usually gets the solution in a series form. In this paper, we propose an efficient modification of ADM, namely two-step Adomian decomposition method (TSADM), that will facilitate the calculations. We then conduct a comparative study between the TSADM and previous methods with the help of several illustrative examples. The results obtained indicate that the TSADM is effective and promising.