Solution of Higher-Order, Multipoint, Nonlinear Boundary Value Problems with High-Order Robin-Type Boundary Conditions by the Adomian Decomposition Method

Authors

Randolph Rach, Emeritus, 316 South Maple Street, Hartford, MI 49057-1225, U.S.A.Follow
Jun-Sheng Duan, School of Sciences, Shanghai Institute of Technology, Shanghai 201418, P.R. ChinaFollow
Abdul-Majid Wazwaz, Department of Mathematics, Saint Xavier University, Chicago, IL 60655, U.S.A.Follow

Author Country (or Countries)

U.S.A.

Abstract

In this paper, we propose a new modified recursion scheme for the approximate solution of higher-order, multipoint, nonlinear boundary value problems with higher-order Robin-type boundary conditions by the Adomian decomposition method. Our new approach utilizes all of the boundary conditions to derive an equivalent nonlinear Fredholm-Volterra integral equation before establishing the new modified recursion scheme for the solution. We solve several complex numerical examples obtaining a rapidly convergent sequence of analytic functions as the solution. In all cases investigated, we achieved an approximately exponential rate of convergence, thus confirming that only a few terms of the Adomian decomposition series can provide an accurate engineering model for parametric simulations.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100403

Recommended Citation

Rach, Randolph; Duan, Jun-Sheng; and Wazwaz, Abdul-Majid (2016) "Solution of Higher-Order, Multipoint, Nonlinear Boundary Value Problems with High-Order Robin-Type Boundary Conditions by the Adomian Decomposition Method," Applied Mathematics & Information Sciences: Vol. 10: Iss. 4, Article 3.
DOI: http://dx.doi.org/10.18576/amis/100403
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss4/3