A new high-order numerical method for solving singular two-point boundary value problems

• Published in: Journal of computational and applied mathematics Vol. 343; pp. 556 - 574
• Main Authors: Roul, Pradip, Thula, Kiran
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2018
• Subjects: Convergence analysis; Equilibrium of the isothermal gas sphere; Error estimation; Optimal quartic B-spline collocation; Singular boundary value problems; Thermal explosion; Equilibrium of the isothermal gas sphere; 34B16; Optimal quartic B-spline collocation; Error estimation; 65L60; Thermal explosion; Singular boundary value problems; 65L10; Convergence analysis
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2018.04.056

Recently, Goh et al. (2012) [28] proposed a numerical technique based on quartic B-spline collocation for solving a class of singular boundary value problems (SBVP) with Neumann and Dirichlet boundary conditions (BC). This method is only fourth-order accurate. In this paper, we propose an optimal numerical technique for solving a more general class of nonlinear SBVP subject to Neumann and Robin BC. The method is based on high order perturbation of the problem under consideration. The convergence of the proposed method is analyzed. To demonstrate the applicability and efficiency of the method, we consider four numerical examples, three of which arise in various physical models in applied science and engineering. A comparison with other available numerical solutions has been carried out to justify the advantage of the proposed technique. Numerical result reveals that the proposed method is sixth order convergent, which in turn is two orders of magnitude larger than in Goh et al. (2012) [28].