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Nonlinear computation. (English) Zbl 0886.34043
This is an expository paper laying the right emphasis on the need to involve nonlinearity in the modelling of natural phenomena so as not to miss features like bifurcation, period doubling and chaos in the computed solutions. Several illustrations are given to show how methods like continuation and branch switching and features like instability and chaos are vital ingredients in the understanding of nature’s functioning.
Computer calculations of nonlinear systems of equations and data handling call for more effort and monitoring of accuracy and ensuring of ‘safety’ of the computed results become more relevant. Errors of computation are usually small compared to errors in simulation and modelling is to be involved as the major source of inaccuracy of the computed results.

MSC:
34C23 Bifurcation theory for ordinary differential equations
65J99 Numerical analysis in abstract spaces
Software:
BIFPACK
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References:
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