On numerical solution of some quasilinear turning point problems. (English) Zbl 0695.65056

Vulanović, Relja

Boundary and interior layers - computational and asymptotic methods, Proc. 5th Int. Conf., BAIL-V, Shanghai/China 1988, Conf. Ser. 12, 368-373 (1988).

[For the entire collection see Zbl 0678.00028.]
Consider the singular perturbed boundary value problem with turning point \(\epsilon^ 2u''+xb(x,u)u'+c(x,u)=0,\quad x\in [-1,1],\) \((u(- 1),u(1))=(A,B),\) where \(\epsilon >0\) is a small parameter, b and c are sufficiently smooth functions, A and B given constants. A finite difference scheme is employed to solve the problem numerically. A special nonequidistant mesh can be chosen which improves the convergence in numerical experiments.

Reviewer: L.J.Grimm

MSC:

65L10	Numerical solution of boundary value problems involving ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34E15	Singular perturbations, general theory for ordinary differential equations

Keywords:

quasilinear; singular perturbations; turning point; small parameter; finite difference scheme; convergence