ODE45 Solve non-stiff differential equations, medium order method.
[TOUT,YOUT] = ODE45(ODEFUN,TSPAN,Y0) integrates the system of
differential equations y' = f(t,y) from time TSPAN(1) to TSPAN(end)
with initial conditions Y0. Each row in the solution array YOUT
corresponds to a time in the column vector TOUT.
* ODEFUN is a function handle. For a scalar T and a vector Y,
ODEFUN(T,Y) must return a column vector corresponding to f(t,y).
* TSPAN is a two-element vector [T0 TFINAL] or a vector with
several time points [T0 T1 ... TFINAL]. If you specify more than
two time points, ODE45 returns interpolated solutions at the
requested times.
* YO is a column vector of initial conditions, one for each equation.
[TOUT,YOUT] = ODE45(ODEFUN,TSPAN,Y0,OPTIONS) specifies integration
option values in the fields of a structure, OPTIONS. Create the
options structure with
odeset.
[TOUT,YOUT,TE,YE,IE] = ODE45(ODEFUN,TSPAN,Y0,OPTIONS) produces
additional outputs for events. An event occurs when a specified function
of T and Y is equal to zero. See
ODE Event Location for details.
SOL = ODE45(...) returns a solution structure instead of numeric
vectors. Use SOL as an input to DEVAL to evaluate the solution at
specific points. Use it as an input to ODEXTEND to extend the
integration interval.
ODE45 can solve problems M(t,y)*y' = f(t,y) with mass matrix M that is
nonsingular. Use ODESET to set the 'Mass' property to a function handle
or the value of the mass matrix. ODE15S and ODE23T can solve problems
with singular mass matrices.
ODE23, ODE45, ODE78, and ODE89 are all single-step solvers that use
explicit Runge-Kutta formulas of different orders to estimate the error
in each step.
* ODE45 is for general use.
* ODE23 is useful for moderately stiff problems.
* ODE78 and ODE89 may be more efficient than ODE45 on non-stiff problems
that are smooth except possibly for a few isolated discontinuities.
* ODE89 may be more efficient than ODE78 on very smooth problems, when
integrating over long time intervals, or when tolerances are tight.
Example
[t,y]=ode45(@vdp1,[0 20],[2 0]);
plot(t,y(:,1));
solves the system y' = vdp1(t,y), using the default relative error
tolerance 1e-3 and the default absolute tolerance of 1e-6 for each
component, and plots the first component of the solution.
Class support for inputs TSPAN, Y0, and the result of ODEFUN(T,Y):
float: double, single
See also ODE23, ODE78, ODE89, ODE113, ODE15S, ODE23S, ODE23T, ODE23TB,
ODE15I, ODESET, ODEPLOT, ODEPHAS2, ODEPHAS3, ODEPRINT, DEVAL,
ODEEXAMPLES, FUNCTION_HANDLE.
Documentation for ode45
doc ode45
Other uses of ode45
dlarray/ode45
