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Domain-Theoretic Formulation of Linear Boundary Value Problems

  • Dirk Pattinson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)

Abstract

We present a domain theoretic framework for obtaining exact solutions of linear boundary value problems. Based on the domain of compact real intervals, we show how to approximate both a fundamental system and a particular solution up to an arbitrary degree of accuracy. The boundary conditions are then satisfied by solving a system of imprecisely given linear equations at every step of the approximation. By restricting the construction to effective bases of the involved domains, we not only obtain results on the computability of boundary value problems, but also directly implementable algorithms, based on proper data types, that approximate solutions up to an arbitrary degree of accuracy. As these data types are based on rational numbers, no numerical errors are incurred in the computation process.

Keywords

Linear Boundary Interval Analysis Fundamental Matrix Fundamental System Domain Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dirk Pattinson
    • 1
  1. 1.Department of ComputingImperial College LondonUK

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