Four-step exponential-fitted methods for nonlinear physical problems

doi:10.1016/S0010-4655(96)00147-6

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Four-step exponential-fitted methods for nonlinear physical problems

1997-02-01

PRE

DOI：10.1016/S0010-4655(96)00147-6

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Abstract

En 中文

We describe a four-step exponential-fitted method for systems of second-order differential equations of the form y '' = f(x,y). This is a sixth-order method depending on five parameters which are automatically adjusted in terms of the equations to be solved. Some other relevant features are as follows: (i) it requires only two solution values to start; (ii) it allows modification of the stepsize during the integration process; (iii) it works in the predictor-corrector mode with only one function evaluation per step; (iv) the whole integration process is controlled in terms of the requested value for the local truncation error. Our method was tested on a representative set of problems taken from physics and found to behave particularly well on the problems involving oscillatory phenomena. A selection of experimental results is given in which our method is compared with a widely used code.

Keywords:

IVP (initial-value problems)

systems of nonlinear second-order ODEs

multistep methods

exponential fitting

predictor-corrector

error control

stepwise control

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