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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Difference methods for problems with different time scales

Author: Robert E. Scheid
Journal: Math. Comp. 44 (1985), 81-92
MSC: Primary 65L05; Secondary 34E20
MathSciNet review: 771032
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Abstract: We consider the use of difference methods for weakly nonlinear systems of ordinary differential equations with rapidly oscillating solutions and develop a general approach which depends only on the smoothness of the coefficients and the nonlinearities. In particular, one is led to a strategy which is suitable for the detection and resolution of turning points in such systems. A computational example is presented.

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Keywords: Difference methods, oscillatory, numerical solution of ordinary differential equations, stiff equations, turning point, resonance
Article copyright: © Copyright 1985 American Mathematical Society