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Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

¹ Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia
² Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia
³ Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia
⁴ Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia

International Journal of Modern Nonlinear Theory and Application·Volume 12 (2023)·Pages 81–98·Published 13 September 2023·DOI10.4236/ijmnta.2023.123006

Abstract

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.

KeywordsLinear Third Order BVPsShooting MethodAdomian Decomposition MethodTwo-Point Boundary Value Problem

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Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

Abstract

References (28)