Geodesic
Overimplicit multistep methods
Applications of Mathematics, Tome 18 (1973) no. 6, pp. 399-421
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The paper is concerned with the numerical solution of ordinary differential equations by a new class of methods called overimplicit multistep methods. The effort is devoted to the study of the convergence and $A$-stability of the introduced methods. $A$-stable formulae of arbitrarily high orders are shown to exist in this new class. This implies the efficiency of using these methods for stiff problems.
The paper is concerned with the numerical solution of ordinary differential equations by a new class of methods called overimplicit multistep methods. The effort is devoted to the study of the convergence and $A$-stability of the introduced methods. $A$-stable formulae of arbitrarily high orders are shown to exist in this new class. This implies the efficiency of using these methods for stiff problems.
DOI : 10.21136/AM.1973.103497
Classification : 65J99, 65L05 
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Práger, Milan; Taufer, Jiří; Vitásek, Emil. Overimplicit multistep methods. Applications of Mathematics, Tome 18 (1973) no. 6, pp. 399-421. doi: 10.21136/AM.1973.103497

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[3] G. Dahlquist: A special stability problem for linear multistep methods. BIT 3 (1963), 27-43. | DOI | MR | Zbl

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[6] J. Taufer (И. Тауфер): Об одном обобщенном многошаговом методе, сб. Применение функциональных методов к краевым задачам математической физики. Новосибирск (1972). | Zbl

[7] R. S. Varga: Matrix iterative analysis. Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1962). | MR

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