Geodesic
Generalized periodic overimplicit multistep methods (GPOM methods)
Applications of Mathematics, Tome 24 (1979) no. 4, pp. 250-272

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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.
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.
DOI : 10.21136/AM.1979.103805
Classification : 65L05, 65L07
Keywords: periodic overimplicit multistep method; sufficient conditions for convergence 
Ismail, Hassan Nasr Ahmed. Generalized periodic overimplicit multistep methods (GPOM methods). Applications of Mathematics, Tome 24 (1979) no. 4, pp. 250-272. doi: 10.21136/AM.1979.103805
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[1] Práger, Taufer, Vitásek: Overimplicit Multistep Methods. Aplikace matematiky, 18 (1973), 399-421. | MR

[2] Henrici P.: Discrete Variable Methods in Ordinary Differential Equations. John Wiley and Sons, Inc. (1962). | MR | Zbl

[3] Lambert J. D.: Computational Methods in Ordinary Differential Equations. John Wiley and Sons Ltd. (1973). | MR | Zbl

[4] Ralston A.: A First Course in Numerical Analysis. McGraw-Hill, Inc. (1965). | MR | Zbl

[5] Babuška, Práger, Vitásek: Numerical Processes in Differential Equations. SNTL-Publishers of Technical Literature, Prague (1966).

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