On Methods for the Construction of the Boundaries of Sets of Solutions for Differential Equations or Finite-Dimensional Approximations with Input Sets

  • E. Adams
Part of the Computing Supplementum book series (COMPUTING, volume 2)


Collections of linear or nonlinear operator equations Au = f are considered which may represent (i) differential or integral equations or (ii) finite-dimensional approximations. Input sets of coefficients a or data f are admitted. The envelope of the set of solutions is to be constructed where this boundary refers (i) to the ränge of values of the solutions or (ii) to a finite-dimensional space. The construction employs either topological boundary mapping or truncated Taylor expansions. Estimates of the local procedural errors are due to suitable a priori sets and interval mathematics. The relation between local and global error estimates is due to boundary mapping or an auxiliary inverse-monotone operator B. The operator B is constructed for the case of arbitrary linear ordinary differential equations with boundary or initial conditions, provided the admitted A satisfy a mild condition.


Boundary Mapping Operator Equation Remainder Term Discrete Analogy Outer Approximation 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • E. Adams
    • 1
  1. 1.Institut für Angewandte MathematikUniversität KarlsruheKarlsruheFederal Republic of Germany

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