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Bifurcation of the Cubic Map Related to Numerical Errors of a First‐Order Differential Equation
Author(s) -
Klepp H. J.
Publication year - 1994
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19940740106
Subject(s) - iterated function , polygon (computer graphics) , mathematics , bifurcation , stability (learning theory) , differential equation , mathematical analysis , order (exchange) , numerical integration , geometry , physics , computer science , telecommunications , frame (networking) , nonlinear system , quantum mechanics , machine learning , finance , economics
It is shown that the one‐ and two‐dimensional cubic maps can be considered as formulae for the determination of approximations for the solution v = v (t) of the differential equation d v /dt = ‐ v ( v 2 ‐ 1) established with the polygon and mixed polygon method. Periodical and irregular behaviour of the iterates v k of these formulae occur because of the weak stability of these methods, due to too large integration steps, and as a result of starting errors. These properties of the iterates v k are properties of the numerical errors ϵk = v(t k ) − v k , too.
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