A note on an adaptive algorithm based on Chebyshev coefficients for two-point boundary value problems

Golik, Wojciech L. ^[1]
1. [1] University of Missouri
  
  University of Missouri
  
  Township of Columbia, Estados Unidos
Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 17, Nº. 2, 1998, págs. 201-213
Idioma: inglés
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Resumen
- An adaptive version of an algorithm, first described by Greengard and Rokhlin, for numerical solution of two-point boundary value problems is proposed. The algorithm transforms two-point BVPs into integral equations, which are then solved by the Nyström method using Chebyshev quadratures. The dense system of algebraic equations is solved in recursively in O(N) operations. The a posteriori node addition algorithm based on the size of Chebyshev coefficients of the solution approximations yields a robust method. The proposed approach combines the advantages of integral formulation and fast solution of dense linear systems with an automatic resolution of boundary and internal layers.