Modified Laguerre pseudospectral method refined by multidomain Legendre pseudospectral approximation (Q818262)

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.