Numerical Approach to Obtain Solutions of First and Second Painleve Equations

Show simple item record

dc.contributor.author Weliwatta RT
dc.contributor.author Dharmawardane PMN
dc.date.accessioned 2022-01-21T06:59:44Z
dc.date.available 2022-01-21T06:59:44Z
dc.date.issued 2019
dc.identifier.citation Proceedings of the 11th Symposium onApplied Science, Business & Industrial Research – 2019 en_US
dc.identifier.issn 2279-1558
dc.identifier.uri http://repository.wyb.ac.lk/handle/1/3530
dc.description.abstract The Painleve' equation and their solutions are used in describing various phenomina in plasma physics, nonlinear waves, quantum field theory, general relativity, nonlinear optics, fibre optics, etc. Paul Painlevé, French mathematician and politician built Poincaré's work in investigating nonlinear second order ordinary differential equations with or without singularities to classify their analytic properties. In the process, he discovered the Painlevé transcendents, written in terms of entire functions, are solution to nonlinear second order ordinary differential equations with the Painlevé property, the solutions are free from movable singularities. This property is a strong indicator of the integrability. Here, we consider about solving the first and second Painlevé equations by using a new computational approach based on Python programs. First, the solutions of first and second Painlevé equations are expressed as Laurent series expansions. Then recurrence relation is obtained for each equation. Finally, solutions are obtained with use of aforementioned recurrence relations and Python codes. en_US
dc.language.iso en en_US
dc.subject Laurent series expansion en_US
dc.subject Painlevé equations en_US
dc.subject Python codes en_US
dc.subject Recurrence relation en_US
dc.title Numerical Approach to Obtain Solutions of First and Second Painleve Equations en_US
dc.type Article en_US


Files in this item

This item appears in the following Collection(s)

Show simple item record

Search DSpace


Browse

My Account