[MATLAB] Numerical calculation of differential equations and ODE45 parameters

[MATLAB] numerical calculation of differential equation sets

We use the ode45 function When we cannot use dsolve to do symbolic solving.

The function prototype is

[T,y] = Ode45 (odefun,tspan,y0) Example
[t,y] = Ode45 (odefun,tspan,y0,options) Example
[T,y,te,ye,ie] = Ode45 ( odefun,tspan,y0,options)
sol = ode45 (___)

Write the function file first. m as the first parameter of the Ode45 Odefun

Function y = Fun (t,x,flag,k)
%flag are a [] to mark the args

%---------------
%some global setting
lamda=1 ;
%---------------
    y=[x (2) *k,lamda*x (2) * (1-x (1)-X (2))-k*x (2)] ';

End

T is the default argument, and X is a vector of dependent variables. The return value is the first derivative of the corresponding dependent variable vector, or we can write

Function y = Fun (t,x,flag,k)
%flag are a [] to mark the args
%---------------
%some global setting
LAMD a=1;
%---------------
    Y=zero (2,1)
    y (1) =x (2) *k;
    Y (2) =lamda*x (2) * (1-x (1)-X (2))-k*x (2);
End

Then write Ode45

[T,x]=ode45 (' fun ', tspan,[0,x0],[],each);

Tspan for [0:10] argument range
The third parameter is the initial value vector
The fourth parameter empty array is used as flag to distinguish the parameters of the incoming fun and the parameters required for Ode45