Abstract
Numerical treatment of fourth-order singular boundary value problems using new quintic B-spline approximation technique
Highlights
Singular boundary value problems (SBVPs) are cropped up in mathematical modeling of many real-life phenomena such as chemical reactions, electrohydrodynamics, aerodynamics, thermal explosions, fluid dynamics, and atomic nuclear reactions
*In this work, we have considered the following class of fourth-order SBVPs
We have explored the approximate solution of fourth-order SBVP's by dint of quintic B-spline (QnBS) functions reinforced with a new approximation for fourth-order derivative
Summary
Khuri (2001) explored the numerical solution of generalized Lane-Emden type equations by means of a new decomposition method based on Adomian polynomials. Taiwo and Hassan (2015) presented a new iterative decomposition method to solve higher-order initial and boundary value problems. The numerical solution to fourth-order Emden-Flower type equations has been discussed in Wazwaz et al (2015) using the Adomian decomposition method. The spline interpolating functions have been employed frequently for solving initial and boundary value problems (BVP's). The fourth-degree polynomial spline functions were utilized by Akram (2011) for the numerical solution of third-order self-adjoint singularly perturbed BVP's. Lodhi and Mishra (2016) employed the quintic B-spline (QnBS) collocation method for solving fourth-order singularly perturbed SBVP's.
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