Mathematica incorporates the latest algorithms for solving industrial-scale linear systems, automatically switching between optimal dense and sparse algorithms—and handling ...

Mathematica's handling of polynomial systems is a tour de force of algebraic computation. Building on mathematical results spanning more than a century, Mathematica for the ...

SemialgebraicComponentInstances[ineqs, {x_1, x_2, ...}] gives at least one sample point in each connected component of the semialgebraic set defined by the inequalities ineqs ...

Mathematica provides an extensive suite of built-in functionality to carry out analysis, design, and simulation of continuous- and discrete-time control systems using both ...

[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. ...

Numerical solution of differential equations. This generates a numerical solution to the equation y^′(x)y(x) with 0<x<2. The result is given in terms of an ...

A Frobenius equation is an equation of the form where a_1, …, a_n are positive integers, m is an integer, and the coordinates x_1, …, x_n of solutions are required to be ...

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 ...

NSolve gives you a general way to find numerical approximations to the solutions of polynomial equations. Finding numerical solutions to more general equations, however, can ...