The Order of Numerical Methods for Ordinary Differential Equations

The Order of Numerical Methods for Ordinary Differential Equations

For a general class of methods, which includes linear multistep and RungeKutta methods as special cases, a concept of order relative to a given starting procedure is defined and an order of convergence theorem is proved. The definition is given an algebraic interpretation and illustrated by the derivation of a particular fourth-order method.

Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

Numerical Methods for Ordinary Differential Equations

Parallel Methods for the Numerical Integration of Ordinary Differential Equations

Abstract. In this paper we derive a class of numerical integration formulas of a parallel type for ordinary differential equations. These formulas may be used simultaneously on a set of arithmetic processors to increase the integration speed. Conditions for the convergence of such formulas are formulated. Explicit examples for two and four processor cases are derived. Results of numerical exper...

Dynamics of numerical Methods for cosymmetric Ordinary differential equations

The dynamics of numerical approximation of cosymmetric ordinary differential equations with a continuous family of equilibria is investigated. Nonconservative and Hamiltonian model systems in two dimensions are considered and these systems are integrated with several firstorder Runge–Kutta methods. The preservation of symmetry and cosymmetry, the stability of equilibrium points, spurious soluti...