Abstract
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.
This paper is dedicated to Prof. Dr. H. Görtier on the occasion of his 70th birthday. — The research was supported by the NATO Senior Fellowship Award SA.5-2-03B(112)961(78)MDL.
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Adams, E. (1980). On Methods for the Construction of the Boundaries of Sets of Solutions for Differential Equations or Finite-Dimensional Approximations with Input Sets. In: Alefeld, G., Grigorieff, R.D. (eds) Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis). Computing Supplementum, vol 2. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8577-3_1
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DOI: https://doi.org/10.1007/978-3-7091-8577-3_1
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