A novel approach for the solution of 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.…”

Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

“…It is observed from the comparison of the absolute errors in Table 4 and the maximum absolute errors in Table 5 that the proposed method based on heuristic computing yields the approximate numerical solution of the problem given by (11)-(12) with greater accuracy. Furthermore it is evident from comparison of Table 4 that the errors relative to the exact solutions by the proposed heuristic hybrid schemes are much smaller than the errors by the approach I method used in [13], whereas they are relatively smaller than approach II method errors given in [13]. Moreover it is observed from the comparison of Table 5 that the maximum errors by the proposed method using hybrid schemes are comparable to B-spline method given in [14].…”

“…We consider the following special case of (1) which arises in thermal explosions [13, 14]: $\begin{array}{c}{y}^{\mathrm{\prime \prime }}+\frac{\mathrm{1}}{x}{y}^{\prime }={-e}^y\end{array}$ subject to the boundary conditions $\begin{array}{c}{y}^{\prime }\left(\mathrm{0}\right)=\mathrm{0},\hspace{1em}\hspace{1em}\mathrm{\hspace{0.17em}\hspace{0.17em}}y\left(\mathrm{1}\right)=\mathrm{0}.\end{array}$ The exact solution of (11) is given by y ( x ) = 2ln⁡(( c + 1)/( cx 2 + 1))⁡, where c = 3 − 2√2.…”

Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

“…Consider the following nonlinear SBVPs [3]: $\begin{array}{c}{\left(x{y}^{\prime }\left(x\right)\right)}^{\prime }=-x{e}^{y\left(x\right)},\hspace{1em}\mathrm{0}<x<\mathrm{1},\\ y^{\prime }\left(\mathrm{0}\right)=\mathrm{0},\hspace{1em}\hspace{1em}y\left(\mathrm{1}\right)=\mathrm{0}.\end{array}$ The analytical solution is y ( x ) = 2ln⁡(( C + 1)/( Cx 2 + 1)), where $C=\mathrm{normal3}-\mathrm{normal2}\sqrt{\mathrm{2}}$.…”

“…Recently, many researchers [3, 4, 12–23] have applied the ADM to deal with many different scientific models. According to the ADM we rewrite (1) in a operator form as $\begin{array}{c}Ly\left(x\right)=f\left(x,y\left(x\right)\right),\end{array}$ where L = x − α d / dx ( x α d / dx ) is a second-order linear differential operator.…”