Conservation laws and the numerical solution of ODEs. II
The author discusses practical aspects of applying his coordinate projection method to approximate the solution of ordinary differential equations with side conditions using multistep difference approximations with variable stepsize [cf. part I, ibid. Part B 12, 1287-1296 (1986; Zbl 0641.65057) and the author's book ``Numerical solution of ordinary differential equations'' (1994; Zbl 0832.65063), Chapter 5]. In the coordinate projection method the value \(y^*_n\) at the \(n\)th step of the solution of the unconstrained problem is projected onto the manifold spanned by the side conditions \(y_n= Py^*_n\) to produce a solution of the constrained problem. It is shown that an asymptotic estimate of the global error of the constrained problem is obtained as the projection of the asymptotic estimate of the unconstrained problem, a result obtained by \textit{E. Eich} for backward difference algorithms [SIAM J. Numer. Anal. 30, No. 5, 1467-1482 (1993; Zbl 0785.65079)]. Methods for coding Runge-Kutta algorithms and difficulties with stiff problems are discussed. Codes have been written for introduction of side conditions into ordinary differential problem solvers from the MATLAB ODE Suite. These are ODE 23, ODE 45, ODE 113, ODE 15s. Results of numerical experiments with ODE 45 and ODE 113 are present.
scientific article; zbMATH DE number 1391609
scientific article