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Zbl 0642.65062
Iyengar, S.R.K.; Jain, Pragya
Spline finite difference methods for singular two point boundary value problems.
(English)
[J] Numer. Math. 50, 363-376 (1987). ISSN 0029-599X; ISSN 0945-3245/e

The authors consider the following class of singular two-point boundary value problems $x\sp{-\alpha}(x\sp{\alpha}u')'=f(x,u),$ $0<x\le 1$ with $u(0)=A$, $u(1)=B$ or $u'(0)=0$, $u(1)=B$. Here $\alpha\in (0,1)$ or $\alpha$ takes values 1 or 2, f may be continuous, $\partial f/\partial u$ may exist, be continuous and $\partial f/\partial u\ge 0$. Then - as is well known - the boundary value problem has a unique solution. For the solution of these problems the authors construct splines and three-point finite difference methods using these splines. They show that such schemes are of $O(h\sp 2)$ under appropriate conditions. The advantage of such spline approximation is that the boundary value problem may be solved with a particular steplength h whereas intermediate values can be computed using the spline. On the basis of some numerical experiments the authors conclude that the discussed methods are robust and give good approximations at the intermediate points.
MSC 2000:
*65L10 Boundary value problems for ODE (numerical methods)
34B15 Nonlinear boundary value problems of ODE

Keywords: singular two-point boundary value problem; numerical examples; splines; three-point finite difference methods; numerical experiments

Cited in: Zbl 0995.65081 Zbl 0665.65067

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