Differential Equation Solving

ODE solvers solve an equation or system of equations for an unknown functions of one variable. PDE solvers solve for functions of two variables (1-D PDEs). The Odesolve and Pdesolve functions are used within solve blocks, allowing for natural notation. The command line functions can be used within programs for iterative calculations.

Ordinary Differential Equations

Odesolve Natural notation ODE solver for Solve Blocks.

rkfixed, Rkadapt, and Bulstoer 4th-order Runge Kutta method, with fixed and adaptive step size, and Bulstoer method for smoothly varying ODEs.

Radau, Stiffb, and Stiffr RADAU, Bulirsch-Stoer, and Rosenbrock methods for stiff systems.

Lowercase ODE function versions to solve only for the last point on the integration interval, saving processing time and reducing memory consumption.

bvalfit, sbval Boundary-value problems, where not all initial conditions are known, converted to initial value problems by linear shooting.

There are also a variety of special polynomial generators and hypergeometric functions which solve specific, common ODEs.

Partial Differential Equations

Pdesolve Natural notation PDE solver for hyperbolic and parabolic systems of 1-D PDEs, including coupled ODEs and algebraic constraints.

numol Command-line solver for hyperbolic and parabolic systems of 1-D PDEs, including coupled ODEs and algebraic constraints.

relax, multigrid Command-line solvers for Poisson's/Laplace's elliptic PDE.