New numerical solutions for solving Kidder equation by using the rational Jacobi functions

In this paper, a new method based on rational Jacobi functions (RJ) is proposed that utilizes quasilinearization method to solve non-linear singular Kidder equation on unbounded interval. The Kidder equation is a second order non-linear two-point boundary value ordinary differential equation on unbo...

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Bibliographic Details
Published in:SeMA journal 2017-12, Vol.74 (4), p.569-583
Main Authors: Parand, Kourosh, Mazaheri, Pooria, Delkhosh, Mehdi, Ghaderi, Amin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Collocation methods
Differential equations
Mathematics
Mathematics and Statistics
Ordinary differential equations
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Summary:In this paper, a new method based on rational Jacobi functions (RJ) is proposed that utilizes quasilinearization method to solve non-linear singular Kidder equation on unbounded interval. The Kidder equation is a second order non-linear two-point boundary value ordinary differential equation on unbounded interval [ 0 , ∞ ) . The equation is solved without domain truncation and variable changing. First, the quasilinearization method is used to convert the equation to sequence of linear ordinary differential equations. Then, by using RJ collocation method equations are solved. For the evaluation, comparison with some numerical solutions shows that the proposed solution is highly accurate. Using 200 collocation points, the value of initial slope that is important is calculated as - 1.1917906497194217341228284 for κ = 0.5 .
ISSN:2254-3902
2281-7875
DOI:10.1007/s40324-016-0103-z