INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND - Volume 3, Issue 2 , June 2014

Pages: 82-93

Date of Publication: 01-Jun-2014

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COMPARATIVE STUDY OF TERMINATING NEWTON ITERATIONS: IN SOLVING ODES

Author: Ronald Tshelametse*

Category: Engineering, Science and Mathematics

Abstract:

The paper deals with the numerical solution of IVP’s for systems of stiff ODE’s with particular emphasis on implicit linear multistep methods (LMM), particularly the backward differentiation formulae (BDF). In thispaper we investigate the current strategies that are used to terminate the Newton iterations in the Matlab Code ode15s.We analyse the algorithms for terminating the Newton iterations as implemented in the code ode15s. We conductnumerical experiments to investigate the levels of usage of each strategy in solving various test problems. The experiments reveal the displacement test is oftenmore stringent that other termination strategies