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Ordinary Differential Equations

Ordinary differential equation initial value problem solvers

The Ordinary Differential Equation (ODE) solvers in MATLAB® solve initial value problems with a variety of properties. The solvers can work on stiff or nonstiff problems, problems with a mass matrix, differential algebraic equations (DAEs), or fully implicit problems. For more information, see Choose an ODE Solver.

Functions

Nonstiff Solvers

ode45 Solve nonstiff differential equations — medium order method
ode23 Solve nonstiff differential equations — low order method
ode113 Solve nonstiff differential equations — variable order method

Stiff Solvers

ode15s Solve stiff differential equations and DAEs — variable order method
ode23s Solve stiff differential equations — low order method
ode23t Solve moderately stiff ODEs and DAEs — trapezoidal rule
ode23tb Solve stiff differential equations — low order method

Fully Implicit Solvers

ode15i Solve fully implicit differential equations — variable order method
decic Compute consistent initial conditions for ode15i

Get/Set Options

odeget Extract ODE option values
odeset Create or modify options structure for ODE solvers

Evaluate and Extend Solution

deval Evaluate differential equation solution structure
odextend Extend solution to ODE
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