Mathematics

ODE Function Summary

ODE Initial Value Problem Solvers

The following table lists the initial value problem solvers, the kind of problem you can solve with each solver, and the method each solver uses.

Solver	Solves These Kinds of Problems	Method
ode45	Nonstiff differential equations	Runge-Kutta
ode23	Nonstiff differential equations	Runge-Kutta
ode113	Nonstiff differential equations	Adams
ode15s	Stiff differential equations and DAEs	NDFs (BDFs)
ode23s	Stiff differential equations	Rosenbrock
ode23t	Moderately stiff differential equations and DAEs	Trapezoidal rule
ode23tb	Stiff differential equations	TR-BDF2
ode15i	Fully implicit differential equations	BDFs

ODE Solution Evaluation and Extension

You can use the following functions to evaluate and extend solutions to ODEs.

Function	Description
deval	Evaluate the numerical solution using the output of dde23.
odextend	Extend the solution of an initial value problem for an ODE

ODE Solvers Properties Handling

An options structure contains named properties whose values are passed to ODE solvers, and which affect problem solution. Use these functions to create, alter, or access an options structure.

Function	Description
odeset	Create or alter options structure for input to ODE solver.
odeget	Extract properties from options structure created with odeset.

ODE Solver Output Functions

If an output function is specified, the solver calls the specified function after every successful integration step. You can use odeset to specify one of these sample functions as the OutputFcn property, or you can modify them to create your own functions.

Function	Description
odeplot	Time-series plot
odephas2	Two-dimensional phase plane plot
odephas3	Three-dimensional phase plane plot
odeprint	Print to command window

Initial Value Problems for ODEs and DAEs

Introduction to Initial Value ODE Problems

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