Differential Equation Solving

Ordinary differential equation (ODE) solvers solve an equation or system of equations for an unknown functions of one variable. Partial differential equation (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 remaining functions can be used within programs for iterative calculations.

Ordinary Differential Equations

Odesolve Natural notation ODE solver for solve blocks.

Adams Adams-Bashford methods.

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

BDF Backward differentiation formula methods.

AdamsBDF Determines whether a system is stiff or non-stiff, and calls BDF or Adams accordingly.

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

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

statespace Systems of linear, first-order ODEs.

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.

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