A differential system can sometimes be solved by analytic means. The function DSolve implements many of the known algorithmic techniques. However, differential systems that ...

The Lotka–Volterra system arises in mathematical biology and models the growth of animal species. Consider two species where Y_1(T) denotes the number of predators and Y_2(T) ...

Consider the matrix differential equation where the initial value y_0 y(0)∈^m×p is given. Assume that y_0^Ty_0I, that the solution has the property of preserving ...

Introduction ODE Integration Methods Partial Differential Equations

NDSolve returns solutions as InterpolatingFunction objects. Most of the time, simply using these as functions does what is needed, but occasionally it is useful to access the ...

The numerical method of lines is a technique for solving partial differential equations by discretizing in all but one dimension, and then integrating the semi-discrete ...

The control mechanisms set up for NDSolve enable you to define your own numerical integration algorithms and use them as specifications for the Method option of NDSolve. ...

When a differential system has a certain structure, it is advantageous if a numerical integration method preserves the structure. In certain situations it is useful to solve ...

[AP91] Ascher, U. and L. Petzold. "Projected Implicit Runge–Kutta Methods for Differential Algebraic Equations." SIAM J. Numer. Anal. 28 (1991): 1097–1120. [AP98] Ascher, U. ...

The equations of motion for a free rigid body whose center of mass is at the origin are given by the following Euler equations (see [MR99]). Two quadratic first integrals of ...