Obrechkoff versus super-implicit methods for the integration of Keplerian Orbits
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This paper discusses the numerical solution of first order initial value problems and a special cl&& of &econd order one& (those not containing flr·st derivative). Two classes or rncLhods arc discussed, super-implicit and Obrechkoff. \Ve will show equivalence of super-implicit and Obrechkoff &chemes. The advantage of Obrechkoff met.hocb i& Lhal Lhey itre higl1 order· onc-sl cp rncLhods and t.l1us 1-1rill nol rcq11in: itddit ional sl art.ing valiJCs. On the other hand they will require higher derivatives of the right hand &ide. In case the right hand &ide i& complex, we may prefer s11per-i rnplici L rncl hodH. The H11pcr-i rnplicil methods may in general have a larger error constant, but one can get the same error constant for the cost of an extra future value.
Computers and Mathematics with Ap- plications, special issue on Numerical Methods in Physics, Chemistry and Engineering, T. E. Simos and G. Abdelas (guest editors), 45, (2003), 383–390.
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