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3-point implicit block method for solving ordinary differential equations.

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

A family of multistep methods to integrate orbits on spheres.

Numerische Mathematik

A modified version of explicit Runge-Kutta methods for energy-preserving

Kybernetika

In this paper, Runge-Kutta methods are discussed for numerical solutions of conservative systems. For the energy of conservative systems being as close to the initial energy as possible, a modified version of explicit Runge-Kutta methods is presented. The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method, but it is superior in energy-preserving to the standard one. Comparing the modified Runge-Kutta method with the standard Runge-Kutta method, numerical experiments...

A nonlinear system of differential equations with distributed delays

Programs and Algorithms of Numerical Mathematics

It is well-known that the environments of most natural populations change with time and that such changes induce variation in the growth characteristics of population which is often modelled by delay differential equations, usually with time-varying delay. The purpose of this article is to derive a numerical solution of the delay differential system with continuously distributed delays based on a composition of $p$-step methods ($p=1,2,3,4,5$) and quadrature formulas. Some numerical results are presented compared...

A note concerning Gauss-Jackson method.

Extracta Mathematicae

Specialized literature concerning studies on Orbital Dynamics usually mentions the Gauss-Jackson or sum squared (∑2) method for the numerical integration of second order differential equations. However, as far as we know, no detailed description of this code is available and there is some confusion about the order of the method and its relation with the Störmer method. In this paper we present a simple way of deriving this algorithm and its corresponding analog for first order equations from the...

A note on numerically consistent initial values for high index differential-algebraic equations.

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

A stability analysis for finite volume schemes applied to the Maxwell system

ESAIM: Mathematical Modelling and Numerical Analysis

We present in this paper a stability study concerning finite volume schemes applied to the two-dimensional Maxwell system, using rectangular or triangular meshes. A stability condition is proved for the first-order upwind scheme on a rectangular mesh. Stability comparisons between the Yee scheme and the finite volume formulation are proposed. We also compare the stability domains obtained when considering the Maxwell system and the convection equation.

A sufficient condition for GPN-stability for delay differential equations.

Numerische Mathematik

A zero-dissipative Runge-Kutta-Nyström method with minimal phase-lag.

Mathematical Problems in Engineering

A ($\alpha$)-Stable Linear Multistep Methods for Stiff IVPs in ODEs

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, a class of A($\alpha$)-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number $k\le 3$ and stiffly stable for $k=4,5$ and $6$. Some numerical results are reported to illustrate the method.

About stability estimates and resolvent conditions

Banach Center Publications

Accelerated Runge-Kutta methods.

Discrete Dynamics in Nature and Society

Acceleration of Runge-Kutta integration schemes.

Discrete Dynamics in Nature and Society

Accurate computation of higher Sturm-Liouville eigenvalues.

Numerische Mathematik

Analysis of the linearly implicit mid-point rule for differential- algebraic equations.

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Approximations and error bounds for computing the inverse mapping

Applications of Mathematics

In this paper we propose a procedure to construct approximations of the inverse of a class of ${𝒞}^{m}$ differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.

Asymptotic Error Estimation for One-Step Methods Based on Quadrature.

Aequationes mathematicae

Chebyshevian Multistep Methods for Ordinary Differential Equation.

Numerische Mathematik

Collocation methods for differential-algebraic equations of index 3.

Numerische Mathematik

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