D.R. Will'e, The Numerical Solution of Delay-differential Equations, Ph.D. thesis, Dept of Mathematics, Manchester University (1989). Home/Search Document Not in Database Summary Related Articles Check |
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Unknown - (2000) (Correct)
....is required when progressing from the initial point t = t 0 (see x4) It is well known that the solutions of DDEs can have discontinuities in their derivatives. These can affect stepsize strategies and interpolation accuracy. For this reason, we considered a Runge Kutta technique. See however [17, 19, 20]. We favoured an embedded Runge Kutta formula to control stepsize and the experiments performed here employed the Dormand and Prince fifth , fourth order pair [6] As part of the development of a code, the author sought examples which test or illustrate the limitations of a given algorithm. In ....
D.R. Will'e, The Numerical Solution of Delay-differential Equations, Ph.D. thesis, Dept of Mathematics, Manchester University (1989).
Experiments in stepsize control for Adams linear multistep methods - Willé (2000) Self-citation (Will'e) (Correct)
....is thus given Sequences of constant stepsizes also make way for more efficient ways to evaluate the integration coefficients used to advance the integration and simplify order control. The author s interest in the study of such cases arises in the solution of delaydifferential equations. See [12, 14]. i= Gamma1 (t Gamma t n Gammai ) dt: 5) t n 1 ; t n ; t n Gammak 1 ] here denotes the (k 1) st Newton divided difference through the points f(t i ; y i ) t n 1 ; y n 1 ) i = n; n Gamma k 1g. The required stepsize estimation thus reduces to a problem of the form ....
....in figure 4. To emphasise the speed of the method, only a third order Runge Kutta scheme is used to estimate the stepsize. This choice could be revised in a working code. For reasons of simplicity, and because of the interest of the author in the solution of functional differential equations [7, 12], the above examples all describe order and stepsize decreases. This is, however, not necessary. An application involving potential stepsize and order increases is given in section 11. Further, numerical experience indicates that the estimators proposed in this paper may help to recover an ....
Will'e, D. R. "The numerical solution of delay-differential equations. " PhD thesis, Department of Mathematics, University of Manchester (1989).
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