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Modified Laguerre pseudospectral method refined by multidomain Legendre pseudospectral approximation. (English) Zbl 1087.65079
Consider a differential equation on the half-line like, e.g., $-U''(x) + \lambda U(x) = f(x)$, $U(0) = \lim_{x \to \infty} U(x) = 0$ with some $\lambda > 0$. For the numerical solution of such equations, a two-stage approach is suggested and analyzed. The first stage consists of a variant of the classical pseudospectral method of Laguerre type. This typically provides a highly accurate numerical solution at the collocation points, but not in the intervals between them. Thus a multidomain Legendre method is added in the second stage in order to improve the overall result.

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