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

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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...

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...

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...

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.

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.

In this paper we propose a procedure to construct approximations of the inverse of a class of ${\mathcal{C}}^{m}$ 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.