High-accuracy P-stable Methods for y″ = f(t, y)
- 1 April 1985
- journal article
- research article
- Published by Oxford University Press (OUP) in IMA Journal of Numerical Analysis
- Vol. 5 (2) , 215-220
- https://doi.org/10.1093/imanum/5.2.215
Abstract
We obtain a one-parameter family of sixth-order P-stable methods for the numerical integration of periodic or near-periodic differential equations that are defined by initial-value problems of the form: y” = f(t, y), y(t0)= y0, y′(t0)= y’0. Our P-stable methods are symmetric and involve three function evaluations per step (periteration, in case f(t, y) is non-linear in y). For non-linear problems, starting values for the solution of the implicit equations by modified Newton's method are suggested and illustrated by an example.Keywords
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