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Volume 9, Number 4, 2019, Pages 1242-1260                                                                DOI:10.11948/2156-907X.20180213
On an iterative method for a class of 2 point \& 3 point nonlinear SBVPs
Mandeep Singh,Amit K Verma,Ravi P Agarwal
Keywords:Singular differential equation, quasi-Newton method, Bessel function, modified Bessel function, two point boundary condition, three point boundary condition.
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.
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