Lagrange meshes from nonclassical orthogonal polynomials
D BayePhysique Nucléaire Théorique et Physique Mathématique, Code Postal 229, Université Libre de Bruxelles, B 1050 Brussels, BelgiumM VinckeAIB-Vinçotte Nuclear, Avenue du Roi 157, B 1190 Brussels, Belgium
1999en
ABI
Abstract
The Lagrange-mesh numerical method has the simplicity of a mesh calculation and the accuracy of a variational calculation. A flexible general procedure for deriving an infinity of new Lagrange meshes related to orthogonal or nonorthogonal bases is introduced by using nonclassical orthogonal polynomials. As an application, different Lagrange meshes based on shifted Gaussian functions are constructed. A simple quantum-mechanical example shows that the Lagrange-mesh method may become more accurate than the original variational calculation with a nonorthogonal basis.
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