Displaying similar documents to “One-step methods for ordinary differential equations with parameters”

Explicit two-step Runge-Kutta methods

Zdzisław Jackiewicz, Rosemary Anne Renaut, Marino Zennaro (1995)

Applications of Mathematics

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The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order p ≤ 5 the minimal number of stages for explicit TSRK method of order p is equal to the minimal number of stages for explicit Runge-Kutta method of order p - 1 . Numerical results are presented...

Numerical solution of boundary value problems for selfadjoint differential equations of 2 n th order

Jiří Taufer (2004)

Applications of Mathematics

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The paper is devoted to solving boundary value problems for self-adjoint linear differential equations of 2 n th order in the case that the corresponding differential operator is self-adjoint and positive semidefinite. The method proposed consists in transforming the original problem to solving several initial value problems for certain systems of first order ODEs. Even if this approach may be used for quite general linear boundary value problems, the new algorithms described here exploit...

Generalized periodic overimplicit multistep methods (GPOM methods)

Hassan Nasr Ahmed Ismail (1979)

Aplikace matematiky

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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.

An algebraic approach for solving boundary value matrix problems: existence, uniqueness and closed form solutions.

Lucas A. Jódar Sanchez (1988)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we show that in an analogous way to the scalar case, the general solution of a non homogeneous second order matrix differential equation may be expressed in terms of the exponential functions of certain matrices related to the corresponding characteristic algebraic matrix equation. We introduce the concept of co-solution of an algebraic equation of the type X^2 + A1.X + A0 = 0, that allows us to obtain a method of the variation of the parameters for the matrix case and...