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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.


ode45 Solve nonstiff differential equations — medium order method
ode23 Solve nonstiff differential equations — low order method
ode113 Solve nonstiff differential equations — variable order method
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 — trapezoidal rule + backward differentiation formula
ode15i Solve fully implicit differential equations — variable order method
decic Compute consistent initial conditions for ode15i
odeget Extract ODE option values
odeset Create or modify options structure for ODE solvers
deval Evaluate differential equation solution structure
odextend Extend solution to ODE


Choose an ODE Solver

ODE background information, solver descriptions, algorithms, and example summary.

Summary of ODE Options

Table indicating which options of odeset work with each ODE solver.

ODE Event Location

Detect events during solution of ODE.

Solve Nonstiff ODEs

This page contains two examples of solving nonstiff ordinary differential equations using ode45.

Solve Stiff ODEs

This page contains two examples of solving stiff ordinary differential equations using ode15s.

Solve Differential Algebraic Equations (DAEs)

Solve ODEs with a singular mass matrix.

Nonnegative ODE Solution

This topic shows how to constrain the solution of an ODE to be nonnegative.

Troubleshoot Common ODE Problems

FAQ containing common problems and solutions.

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