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A Numerical Approach to Matrix Linear ODEs in Complex Plane

Summary: A Numerical Approach to Matrix Linear ODEs in
Complex Plane
F. V. Andreev
Western Illinois University
Macomb, IL 61455
E-mail: F-Andreev@wiu.edu
December 20, 2003
A numerical approach to the problem of solving linear ordinary
differential equations of Fuchsian type in complex plane is considered.
An exposition is based on a series of Java applets (written by the au-
thor) that implement the suggested approach. The Java source code
for the ODE solver is published as a supplement to the article. Perfor-
mance results on various platforms are presented and discussed. Then,
computing monodromy matrices is considered. Their normalization is
discussed. Applications to the sixth Painleve equation, in particular
to the case of a Frobenius manifold solution, are discussed.
Short title: Solving matrix ODEs in Complex Plane

Submitted to The LMS Journal of Computation and Mathematics


Source: Andreev, Fedor - Department of Mathematics, Western Illinois University


Collections: Mathematics