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

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 unbounded interval $$[0,\infty )$$ [ 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 $$-1.1917906497194217341228284$$ - 1.1917906497194217341228284 for $$\kappa =0.5$$ κ = 0.5 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

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

, Volume 74 (4) – Jan 9, 2017
15 pages

Publisher
Springer Journals
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0103-z
Publisher site
See Article on Publisher Site

### Abstract

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 $$[0,\infty )$$ [ 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 $$-1.1917906497194217341228284$$ - 1.1917906497194217341228284 for $$\kappa =0.5$$ κ = 0.5 .

### Journal

SeMA JournalSpringer Journals

Published: Jan 9, 2017

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