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Oscillation analysis of numerical solutions in the θ ‐methods for differential equation of advanced type
Author(s) -
Gao Jianfang,
Liu Shimeng
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3458
Subject(s) - oscillation (cell signaling) , mathematics , piecewise , numerical analysis , type (biology) , differential equation , mathematical analysis , constant (computer programming) , computer science , ecology , genetics , biology , programming language
The paper deals with the oscillation analysis of numerical solution in the θ ‐methods for differential equations with piecewise constant arguments of advanced type. The conditions of the oscillation for the θ ‐method are obtained. It is proved that the oscillation of the analytic solution is preserved by the θ ‐ method. Some numerical experiments are given. Copyright © 2015 John Wiley & Sons, Ltd.