Recursive Collocation for the Numerical Solution of Stiff Ordinary Differential Equations

Recursive Collocation for the Numerical Solution of Stiff Ordinary Differential Equations

The exact solution of a given stiff system of nonlinear (homogeneous) ordinary differential equations on a given interval / is approximated, on each subinterval ak corresponding to a partition ttk of /, by a linear combination Uk(x) of exponential functions. The function Uk(x) will involve only the "significant" eigenvalues (in a sense to be made precise) of the approximate Jacobian for <sk. Th...

Error Estimation for Collocation Solution of Linear Ordinary Differential Equations

This paper is concerned with error estimates for the numerical solution of linear ordinary differential equations by global or piecewise polynomial collocation which are based on consideration of the differential operator involved and related matrices and on the residual. It is shown that a significant advantage may be obtained by considering the form of the residual rather than just its norm.

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...

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