Author(s)

Nawal Al-Zaid, Kholoud Alzahrani, Huda Bakodah^*, Mariam Al-Mazmumy

Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia.

The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.

Linear Third Order BVPs, Shooting Method, Adomian Decomposition Method, Two-Point Boundary Value Problem

Al-Zaid, N. , Alzahrani, K. , Bakodah, H. and Al-Mazmumy, M. (2023) Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems. International Journal of Modern Nonlinear Theory and Application, 12, 81-98. doi: 10.4236/ijmnta.2023.123006.