Solves a first order differential-algebraic system of equations, g(t, y, y') = 0, using the Petzold-Gear BDF method.

Solves a generalized Feynman-Kac equation on a finite interval using Hermite quintic splines.

Computes the value of a Hermite quintic spline or the value of one of its derivatives.

Adams-Gear or Runge-Kutta method.

Solves a general system of ordinary differential equations.

Solves a system of partial differential equations.

Solves a system of partial differential equations of the form ut = f(x, t, u, ux, uxx) using the method of lines.

The solution is represented with cubic Hermite polynomials.

Solves Poisson's or Helmholtz's equation on a two-dimensional rectangle using a fast Poisson solver based on the HODIE finite-difference scheme on a uniform mesh.