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Product quasi-interpolation method for weakly singular integral equation eigenvalue problem

Author

Listed:
  • Sablonnière, P.
  • Sbibih, D.
  • Tahrichi, M.

Abstract

A discrete method of accuracy O(hm) is constructed to solve the integral equation eigenvalue problem λϕ(x)=∫−11K(x,y)ϕ(y)dy, where K(x, y)=log|x−y| or K(x, y)=|x−y|−α, 0<α<1, ϕ(x) being the eigenfunction associated with the eigenvalue λ. The method is based first on improving the boundary behavior of the exact solution ϕ(x) with the help of a change of variables, and second on the product integration method based on a discrete spline quasi-interpolant (abbr. dQI) of order m.

Suggested Citation

  • Sablonnière, P. & Sbibih, D. & Tahrichi, M., 2011. "Product quasi-interpolation method for weakly singular integral equation eigenvalue problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2337-2345.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:10:p:2337-2345
    DOI: 10.1016/j.matcom.2010.12.018
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