Previous |  Up |  Next


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.
[1] I. Babuška M. Práger, E. Vitásek: Numerical processes in differential equations. Interscience publishers, London, New York, Sydney (1966). MR 0223101
[2] G. Birkhoff, R. S. Varga: Discretization errors for well-set Cauchy problems I. J. Math, and Phys. 44 (1965), 1-23. MR 0179952 | Zbl 0134.13406
[3] G. Dahlquist: A special stability problem for linear multistep methods. BIT 3 (1963), 27-43. DOI 10.1007/BF01963532 | MR 0170477 | Zbl 0123.11703
[4] F. R. Gantmacher (Ф. Р. Гантмахер): Теория матриц. Наука, Москва (1966). Zbl 0136.00410
[5] P. Henrici: Discrete variable methods in ordinary differential equations. J. Wiley & Sons, Inc., New York, London (1962). MR 0135729 | Zbl 0112.34901
[6] J. Taufer (И. Тауфер): Об одном обобщенном многошаговом методе, сб. Применение функциональных методов к краевым задачам математической физики. Новосибирск (1972). Zbl 0262.65050
[7] R. S. Varga: Matrix iterative analysis. Prentice-Hall, Inc., Englewood Cliffs, New Jersey (1962). MR 0158502
[8] E. Vitásek (E. Витасек): Строго неявные методы для решения дифференциальных уравнений. сб. Применение функциональных методов к краевым задачам математической физики, Новосибирск (1972).
Partner of
EuDML logo