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
• DOI: 10.22199/S07160917.1998.0002.00005
• Enlaces
  • Texto completo
• 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.

• Referencias bibliográficas
  • Citas [1] L. Greengard and V. Rokhlin. On the Numerical Solution of Two-Point Boundary Value Problems. Communications on Pure and Applied...
  • [2] C. T. H. Baker. The Numerical Treatment of Integral Equations. Clarendon Press, Oxford, (1977).
  • [3] C. W. Clenshaw and A. R. Curtis. A method for numerical integration on an automatic computer. Numer. Math., 2 : pp. 197-205, (1960).
  • [4] U. M. Ascher, R. M. M. Matheij, and R. D. Russell. Numerical solution of boundary value problems for ordinary dfferential equations. Series...
  • [5] J. R. Cash. On the numerical integration of nonlinear two point bound-ary value problems using iterated deferred corrections, Part II....