$RungeKuttaMethod is a global environment setting, specifying the type of method to be generated by ButcherPhi and related functions.

The general form of an ODE with order n is As in the case of second-order ODEs, such an ODE can be classified as linear or nonlinear. The general form of a linear ODE of ...

This equation is solved by simply integrating the right-hand side with respect to x. Here is a plot of the integral curves for different values of the arbitrary constant C[1].

Searching for local minima and maxima. This finds the value of x which minimizes Γ(x), starting at x2. The last element of the list gives the value at which the minimum is ...

One-dimensional Laplace transforms. The Laplace transform of a function f(t) is given by ∫_0^∞f(t)e^-stt. The inverse Laplace transform of F(s) is given for suitable γ by ( ...

The functions FindMinimum, FindMaximum, and FindRoot have the HoldAll attribute and so have special semantics for evaluation of their arguments. First, the variables are ...

When numerically solving Hamiltonian dynamical systems it is advantageous if the numerical method yields a symplectic map. If the Hamiltonian can be written in separable ...

Mathematica's sophisticated algorithms for handling higher mathematical functions to arbitrary precision—and in symbolic form—immediately brings a new level of accuracy—and ...

 

Mathematica has a collection of commands that do unconstrained optimization (FindMinimum and FindMaximum) and solve nonlinear equations (FindRoot) and nonlinear fitting ...