Non-convergence partitioning strategy for solving van der Pol's equations

• Published in: AIP Conference Proceedings
• Main Author: Othman K.I.; Suleiman M.; Ibrahim Z.B.
• Format: Conference paper
• Language: English
• Published: American Institute of Physics Inc. 2018
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85051134473&doi=10.1063%2f1.5045407&partnerID=40&md5=30991a275cbd5f05b09ee9d814a99739

Partitioning is a strategy that will reduce computational cost. Starting with all equations be treated as non-stiff, this strategy will divide the equations into the stiff and nonstiff subsystem. The non-convergence partitioning strategy will determine equations that caused instability, and put the equations into stiff subsystem and solved using Newton iteration backward differentiation formulae and all other equations remain in the non-stiff subsystem and solved by Adams method. This partitioning strategy will continue until instability occurs again and placed equations that caused instability into the stiff subsystem. But for van der Pol equation, the nature of the equations need to change from stiff to the non-stiff subsystem and vice versa when it is necessary. This paper will extend the non-convergence partitioning strategy by allowing equations from the stiff subsystem to be placed back in the non-stiff subsystem. © 2018 Author(s).