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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
Author(s) -
Roul Pradip,
Kumari Trishna,
Prasad Goura VMK
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6947
Subject(s) - mathematics , singular boundary method , mathematical analysis , boundary value problem , robin boundary condition , neumann boundary condition , nonlinear system , finite element method , boundary element method , physics , quantum mechanics , thermodynamics
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.