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Damping and phase analysis for some methods for solving second‐order ordinary differential equations
Author(s) -
Gladwell I.,
Thomas R. M.
Publication year - 1983
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620190404
Subject(s) - ordinary differential equation , mathematics , oscillation (cell signaling) , differential equation , oscillation theory , numerical methods for ordinary differential equations , mathematical analysis , numerical analysis , phase (matter) , runge–kutta methods , exact differential equation , differential algebraic equation , physics , genetics , biology , quantum mechanics
We consider numerical methods for initial value problems for second‐order systems of ordinary differential equations, analysing them by applying them to the test equation We discuss conditions which ensure an oscillatory numerical solution and the desirability of such a property. We also use a slightly more general test equation to derive conditions which ensure that the numerical forced oscillation is in phase with the true forced oscillation. To illustrate the theory, we consider the damping and phase properties of some frequently used methods.