Numerical solution of Cauchy problems with multiple poles of integer order

Abstract

We consider Cauchy problem for ordinary differential equation with solution possessing a sequence of multiple poles. We propose the generalized reciprocal function method. It reduces calculation of a multiple pole to retrieval of a simple zero of accordingly chosen function. Advantages of this approach are illustrated by numerical examples. We propose two representative test problems which constitute interest for verification of other numerical methods for problems with poles.

Keywords

• cauchy problem
• singularities
• continuation through a pole
• multiple poles