On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology

An efficient wavelet based spectral method to singular boundary value problems

“…The numerical study of singular boundary value problems arising in various physical models has been done by many authors [1][2][3][4][5][6][7][8][9][10][11] and a variety of methods have been introduced to solve such singular boundary B G. Hariharan hariharang2011@gmail.com 1 Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur, Tamilnadu 613 401, India value problems [2,3,5,[8][9][10]. Although, these numerical methods have many advantages, but a huge amount of computational work is needed.…”

Variational Iteration Method for Nonlinear Singular Two-Point Boundary Value Problems Arising in Human Physiology

“…For the two examples shown in Section 3, the second and third iteration solutions obtained by the VIM were substantially more accurate than the 16 and the 32 time-step approximate solutions obtained by cubic B-spline and the �nite difference methods. Present method Method in [9] Method in [3] . …”

“…It is also assumed that ( ) and / are both continuous on [0 ] × ℝ and further / 0. Assuming that / is analytic in | | for some , the existence-uniqueness has been established for problem (1) under the following restrictions (see [3] and the references therein):…”

“…Problems (1)- (2) and (1)- (3) have been treated by several authors using different numerical schemes such as cubic Bsplines, �nite difference, and pointwise solution bounds [3,8,9]. e VIM has been used by Wazwaz [10] to solve the nonlinear singular Emden-Fowler boundary value problem, which is a special case of (1)- (2), where ( ) = .…”

Computational technique for singular boundary value problems by using Numerical Quadrature

“…Attempts by many researchers for the removal of singularity are based on using the series expansion procedures in the neighborhood ( , ) 0 δ of singularity (δ is vicinity of the singularity) and then solving the regular boundary value problem in the interval ( , ) δ 1 using any numerical method. Pandey and Singh [14] have used a finite difference method based on uniform mesh for a class of singular boundary value problems. Ravikanth and Reddy [15] have discussed a numerical method by using Chebyshev economization in the vicinity of the singularity for solving boundary value problems with regular singularity.…”