An efficient numerical method based on exponential B‐spline basis functions for solving a class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions

• Published in: Mathematical methods in the applied sciences Vol. 44; no. 5; pp. 3376 - 3395
• Main Authors: Roul, Pradip, Kumari, Trishna, Prasad Goura, VMK
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.03.2021
• Subjects: Basis functions; Boundary conditions; Boundary value problems; Collocation methods; convergence analysis; Differential equations; exponential cubic B‐spline collocation; Finite difference method; isothermal gas sphere; Mathematical analysis; Numerical analysis; Numerical methods; oxygen diffusion problem; singular boundary value problem; thermal explosion
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.6947

In this paper, we develop a numerical scheme to approximate the solution of a general class of nonlinear singular boundary value problems (SBVPs) subject to Neumann and Robin boundary conditions. The original differential equation has a singularity at the point x=0, which is removed via L'Hospital's law with an assumption about the derivative of the solution at the point x=0. An exponential B‐spline collocation approach is then constructed to solve the resulting boundary value problem. Convergence analysis of the method is discussed. Numerical examples are provided to illustrate the applicability and efficiency of the method. Our results are compared with those obtained by other three numerical methods such as uniform mesh cubic B‐spline collocation (UCS) method, nonstandard finite difference method, and finite difference method based on Chawla's identity.