Fifth step block method and shooting constant for third order nonlinear dynamical systems

• Published in: International journal of system assurance engineering and management Vol. 15; no. 6; pp. 2218 - 2229
• Main Authors: Jena, Saumya Ranjan, Sahu, Itishree, Paul, Arjun Kumar
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.06.2024; Springer Nature B.V
• Subjects: Boundary conditions; Boundary value problems; Differential equations; Dynamical systems; Engineering; Engineering Economics; Logistics; Marketing; Methods; Nonlinear systems; Ordinary differential equations; Organization; Original Article; Quality Control; Reliability; Safety and Risk; Taylor series; 65L05; Shooting constants and stability; 65L010; Boundary conditions; Fifth step block method; Modified Taylor series scheme
• ISSN: 0975-6809; 0976-4348
• DOI: 10.1007/s13198-023-02237-z

In this paper, the approximate solution of a set of nonlinear third order differential equations with mixed boundary conditions is obtained by employing the fifth step block method and Modified Taylor Series Scheme (MTSS). The motivation of this subject to implement MTSS for determining the shooting constants associated with the Initial Value Problems (IVPs) rather than Boundary Value Problems (BVPs). The fifth step block method is also used to solve nonlinear third Order Differential Equations (ODEs) on the definite interval. Two numerical examples are experimented to demonstrate the efficiency and accuracy of the proposed scheme by obtaining the absolute errors. Furhter, the order, convergence and stability of the proposed method are discussed to strengthen the theoretical concept.