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Interval Computations and Differential Equations

Petr Girg
Organization: University of West Bohemia

Wolfram Technology Conference 2011
Conference location

Champaign, Illinois, USA

Interval computations are becoming a well-accepted method of rigorous mathematical proofs. We discuss some possibilities of deploying Mathematica into interval-computation proofs of theorems concerning boundary-value problems for strongly nonlinear differential equations. Alternatively, we also describe development of a highly optimized library supporting special functions from the theory of nonlinear differential equations. For performance and correctness reasons, our library is written in GNU Assembler for Intel Pentium. We use new LibraryLink Mathematica 8 technology for calling user-defined C functions. A C interface is used for accessibility of our library functions from Mathematica. In order to improve performance of our library, we derived various approximate formulas for our special functions using symbolic calculations. The library will be used in proving theorems in the theory of nonlinear differential equations.

IntervalComputationsAndDifferentialEquations.nb (23.8 MB) - Mathematica Notebook
IntervalComputationsAndDifferentialEquations.cdf (23.8 MB) - CDF Document

*Wolfram Technology