ON AN ITERATIVE METHOD FOR A CLASS OF 2 POINT &amp; 3 POINT NONLINEAR SBVPS

Mandeep Singh; Amit Kumar Verma; Ravi P. Agarwal

doi:10.11948/2156-907X.20180213

2019 Volume 9 Issue 4

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Mandeep Singh, Amit Kumar Verma, Ravi P. Agarwal. ON AN ITERATIVE METHOD FOR A CLASS OF 2 POINT & 3 POINT NONLINEAR SBVPS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1242-1260. doi: 10.11948/2156-907X.20180213

Citation:

Mandeep Singh, Amit Kumar Verma, Ravi P. Agarwal. ON AN ITERATIVE METHOD FOR A CLASS OF 2 POINT & 3 POINT NONLINEAR SBVPS[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1242-1260. doi: 10.11948/2156-907X.20180213

ON AN ITERATIVE METHOD FOR A CLASS OF 2 POINT & 3 POINT NONLINEAR SBVPS

1.
Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Solan, HP-173234, India
2.
Department of Mathematics, IIT Patna, Bihta, Patna, Bihar 801106, India
3.
Department of Mathematics, Texas A & M, University-Kingsville, 700 University Blvd., MSC 172, Kingsville, Texas 78363-8202

Corresponding author: Email address:akverma@iitp.ac.in(Amit K. Verma)

Abstract

Abstract

In this article, we propose a novel modification to Quasi-Newton method, which is now a days popularly known as variation iteration method (VIM) and use it to solve the following class of nonlinear singular differential equations which arises in chemistry $ -y''(x)-\frac{\alpha}{x}y'(x) = f(x, y), \; x\in(0, 1), $ where $ \alpha\geq1 $, subject to certain two point and three point boundary conditions. We compute the relaxation parameter as a function of Bessel and the modified Bessel functions. Since rate of convergence of solutions to the iterative scheme depends on the relaxation parameter, thus we can have faster convergence. We validate our results for two point and three point boundary conditions. We allow $ \partial f/\partial y $ to take both positive and negative values.
- Singular differential equation /
- quasi-Newton method /
- Bessel function /
- modified Bessel function /
- two point boundary condition /
- three point boundary condition.
MSC: 34B16, 34B27, 34B60

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References

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