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Keywords:
periodic overimplicit multistep method; sufficient conditions for convergence
periodic overimplicit multistep method; sufficient conditions for convergence
Summary:
The paper deals with some new methods for the numerical solution of initial value problems for ordinary differential equations. The main idea of these methods consists in the fact that in one step of the method a group of unknown values of the approximate solution is computed simultaneously. The class of methods under investigation is wide enough to contain almost all known classical methods. Sufficient conditions for convergence are found.
References:
[1] Práger, Taufer, Vitásek: Overimplicit Multistep Methods. Aplikace matematiky, 18 (1973), 399-421. MR 0366041
[2] Henrici P.: Discrete Variable Methods in Ordinary Differential Equations. John Wiley and Sons, Inc. (1962). MR 0135729 | Zbl 0112.34901
[3] Lambert J. D.: Computational Methods in Ordinary Differential Equations. John Wiley and Sons Ltd. (1973). MR 0423815 | Zbl 0258.65069
[4] Ralston A.: A First Course in Numerical Analysis. McGraw-Hill, Inc. (1965). MR 0191070 | Zbl 0139.31603
[5] Babuška, Práger, Vitásek: Numerical Processes in Differential Equations. SNTL-Publishers of Technical Literature, Prague (1966).
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