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 ...

An expression like x^2+2x-7==0 represents an equation in Mathematica. You will often need to solve equations like this, to find out for what values of x they are true. This ...

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

While DSolve usually returns the correct solution to a differential equation it is given, it is common practice to verify the solution returned by any differential equation ...

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

DiscreteLyapunovSolve[a, c] finds the numeric solution x of the discrete matrix equation a.x.a\[ConjugateTranspose] - x == c.DiscreteLyapunovSolve[a, b, c] solves a.x.b - x ...

LyapunovSolve[a, c] finds a solution x of the matrix Lyapunov equation a.x + x.a\[ConjugateTranspose] == c.LyapunovSolve[a, b, c] solves a.x + x.b == c.LyapunovSolve[{a, d}, ...

If you have an equation like 2x==0, it is perfectly clear that the only possible solution is x->0. However, if you have an equation like ax==0, things are not so clear. If a ...

Mathematica 's differential equation solving functions can be applied to many different classes of differential equations, automatically selecting the appropriate algorithms ...