Numerische Mathematik

, Volume 39, Issue 3, pp 341–350

Finite difference methods and their convergence for a class of singular two point boundary value problems

  • M. M. Chawla
  • C. P. Katti
On the Number of Solutions of the Discrete Theodorsen-Equation

DOI: 10.1007/BF01407867

Cite this article as:
Chawla, M.M. & Katti, C.P. Numer. Math. (1982) 39: 341. doi:10.1007/BF01407867


We discuss the construction of three-point finite difference approximations and their convergence for the class of singular two-point boundary value problems: (xαy′)′=f(x,y), y(0)=A, y(1)=B, 0<α<1. We first establish a certain identity, based on general (non-uniform) mesh, from which various methods can be derived. To obtain a method having order two for all α∈(0,1), we investigate three possibilities. By employing an appropriate non-uniform mesh over [0,1], we obtain a methodM1 based on just one evaluation off. For uniform mesh we obtain two methodsM2 andM3 each based on three evaluations off. For α=0,M1 andM2 both reduce to the classical second-order method based on one evaluation off. These three methods are investigated, theirO(h2)-convergence established and illustrated by numerical examples.

Subject Classifications

AMS(MOS): 65L10 CR: 5.17 

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • M. M. Chawla
    • 1
  • C. P. Katti
    • 2
  1. 1.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA
  2. 2.Department of MathematicsIndian Institute of TechnologyNew DelhiIndia

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