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Theory and computation in singular boundary value problems. (English) Zbl 1134.65045
The problem under consideration is the singular boundary value problem $$ (p(x)y')'/p(x) - q(x)y = f(x), \quad x\in(0,1),\quad \lim \limits_{x \to 0^+} p(x)y'(x) = 0, \quad y(1)=0. $$ The author applies and investigates to this problem two numerical methods. The first is the Galerkin method with the base system generated by the sinc function $sinc(x)=sin(\pi x)/(\pi x)$, and the second method is some variant of the well-known parametric continuation method which is developed for boundary value problems in recent works under the denotation “homotopy perturbation method”. A numerical example is given to demonstrate the computational efficiency of the two methods.

65L10Boundary value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B05Linear boundary value problems for ODE
Full Text: DOI
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