Solution of equations: the Newton and reduced method

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

Chapter Chapter 10 in Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming, 2009, pp 247-258 from Springer

Abstract: Abstract The Newton method is an iterative method for the solution of a set of nonlinear equations. In the case of a single variable, the method involves division by a derivative, but in the case of more than one variable the method requires the inversion of the Jacobian matrix, and this can be very time consuming. An introduction will be given to the Newton method. It will be shown that the direct Newton method is equivalent to iterating a set of equations to a time steady state. This correspondence will be used to suggest a reduced Newton method in which matrix inversion is kept to a minimum. It is shown how the variables which arise in device modelling can be grouped conveniently when solving the associated equations using the Newton method.

Date: 2009
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DOI: 10.1007/978-1-84882-937-4_10

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