Functions > Solving and Optimization > Differential Equation Solvers > About Differential Equation Solvers
Ordinary Differential Equation (ODE) solvers solve an equation or system of equations for unknown functions of one variable. Partial Differential Equation (PDE) solvers solve for functions of two variables (1D PDEs).
Ordinary Differential Equations
To solve an ODE directly without creating a solve block, use one of the ODE solvers, which solve systems of ODEs of the following form:
where y is vector of unknown functions of the independent variable x. To solve a higher-order ODE, rewrite it as a system of first order ODEs.
The ODE solvers are divided into two types: solvers for stiff systems and solvers for nonstiff systems. A system of ODEs written in matrix form as y’=Ay, is called stiff if the matrix A is nearly singular. Otherwise, the system is nonstiff.
rkfixed, Rkadapt, Bulstoer—4th order Runge Kutta method, with fixed and adaptive step size, and Bulstoer method for smoothly varying ODEs
BDF—Backward differentiation formula methods