Abstract
The aim of study of this article is to determine the solution of seventh order boundary value problem. The behavior of the induction motor is simulated by fifth order differential equation model and induction machine with two rotor circuits is represented by the seventh order differential equations. In this study, a Reproducing Kernel Method (RKM) for a class of seventh-order nonlinear boundary value problems is investigated. The argument is based on the reproducing kernel space W<sup>8</sup><sub>2</sub> [0, 1]. The proposed method gives better results when compared with the method available in literature (Siddiqi et al., 2012a). Two numerical examples are given to illustrate the implementation and efficiency of the method.
Highlights
5th order differential equation model simulated the behavior of the induction motor which includes two stator state variables, two rotor state variables, and shaft speed
Two more variables must be added to account for the effects of a second rotor circuit representing deep bars, a starting cage, or rotor distributed parameters
The induction machine with two rotor circuits is represented by the seventh order differential equations of flux linkages and speed (Richards and Sarma, 1994)
Summary
5th order differential equation model simulated the behavior of the induction motor which includes two stator state variables, two rotor state variables, and shaft speed. The induction machine with two rotor circuits is represented by the seventh order differential equations of flux linkages and speed (Richards and Sarma, 1994). Siddiqi and Akram (2006, 2007) presented non-polynomial spline method and sextic spline method for the numerical solution of the fifth-order linear special case boundary value problems. Siddiqi et al (2007) developed quintic spline method for the numerical solutions of linear special case sixth-order boundary value problems. In Siddiqi et al (2012a, b) and Siddiqi and Iftikhar (2013a) solutions of seventh order boundary value problems are discussed. Siddiqi and Iftikhar (2013b) presented the solution of higher order boundary value problems using the homotopy analysis method. A reproducing kernel method is used for the solution of linear and nonlinear seventh order BVP.
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