Optimal solution of ordinary differential equations

Matlab : Numerical Solution of Ordinary Differential Equations

Matlab has facilities for the numerical solution of ordinary differential equations (ODEs) of any order. In this document we first consider the solution of a first order ODE. Higher order ODEs can be solved using the same methods, with the higher order equations first having to be reformulated as a system of first order equations. Techniques for solving the first order and second order equation...

On parallel solution of ordinary differential equations

In this paper the performance of a parallel iterated Runge-Kutta method is compared versus those of the serial fouth order Runge-Kutta and Dormand-Prince methods. It was found that, typically, the runtime for the parallel method is comparable to that of the serial versions, thought it uses considerably more computational resources. A new algorithm is proposed where full parallelization is used ...

Numerical solution of ordinary differential equations

Ordinary differential equations are ubiquitous in science and engineering: in geometry and mechanics from the first examples onwards (Newton, Leibniz, Euler, Lagrange), in chemical reaction kinetics, molecular dynamics, electronic circuits, population dynamics, and many more application areas. They also arise, after semidiscretization in space, in the numerical treatment of time-dependent parti...

Numerical Solution of Ordinary Differential Equations

Optimal control of ordinary differential equations

The paper deals with optimal control problems with only onecontrol variable and one state constraint, of arbitrary order. We considerthe case of finitely many boundary arcs and touch times. We obtain a no-gap theory of second-order conditions, allowing to characterize second-orderquadratic growth.