BIT Numerical Mathematics

, Volume 15, Issue 2, pp 136–143 | Cite as

On the approximate solution of the abel integral equation with discontinuous solution

  • H. Brunner


The classical Abel integral equation with discontinuous solution is solved numerically by replacing the inhomogeneous termg(x) (known on some finite subsetZ N of the interval of integration) by a suitable linear familyψ(β, x) of continuous functions. The choice of these functions will be governed by two criteria: they are to reflect the discontinuous behavior of the exact solution of the integral equation, and they are to be such that the problem of finding a best (discrete) Chebyshev approximation tog onZ N possesses a unique solution.


Continuous Function Integral Equation Exact Solution Unique Solution Approximate Solution 
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Copyright information

© BIT Foundations 1975

Authors and Affiliations

  • H. Brunner
    • 1
  1. 1.Department of MathematicsDalhousie UniversityHalifaxCanada

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