Solution of equations: the phaseplane method

E. A. B. Cole ()
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E. A. B. Cole: University of Leeds, Department of Applied Mathematics

Chapter Chapter 11 in Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming, 2009, pp 259-282 from Springer

Abstract: Abstract The phaseplane method is an iterative method which allows the defining equations to be easily modified without having to do much preparatory work, in the form of re-writing of code, for the resulting numerical solutions. Extra variables are defined to enable the system of second order differential equations to be written as a system of first order equations, and the enlarged system is iterated in the phase plane which is spanned by this enlarged set of variables. It is shown how this method can be tailored to the specific needs of device modelling.

Keywords: Equilibrium Point; Newton Method; Phase Plane; Order Differential Equation; Complex Root (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-84882-937-4_11

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DOI: 10.1007/978-1-84882-937-4_11

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