• Corpus ID: 55794893

Numerical Verification Methods for the Solutions of Nonlinear Elliptic and Evolution Problems

  title={Numerical Verification Methods for the Solutions of Nonlinear Elliptic and Evolution Problems},
  author={Mitsuhiro T. Nakao},
  • M. Nakao
  • Published 1 June 1992
  • Mathematics
In this paper, we consider a numerical technique to enclose the solutions with guaranteed error bounds for nonlinear elliptic bundary value problems as well as its extension to the evolution equations. Using a finite element solution and explicit error estimate for certain simple hnear problem, we construct, in computer, a set of functions which satisfies the condition of Schauder’s or other fixed point theorem under some appropriately function spaces. In order to obtain such a numerical set… 
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Non-homogeneous boundary value problems and apphcations I and I I, Springer-Verlag

  • 1972

The finite element method for elhptic

  • 1978

Enclosing the solutions of ordinary initial and boundary value problems, Computerarithmetic(eds

  • 1987