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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.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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References:

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