function main % a simple example to solve ODE's % Uses ODE45 to solve % dx_dt(1) = -1*x(1)-1*x(2) % dx_dt(2) = 1*x(1) -2*x(2) %set an error options=odeset('RelTol',1e-6,'Stats','on'); %initial conditions Xo = [1;1]; %timespan tspan = [0,5]; %call the solver tic [t,X] = ode45(@TestFunction,tspan,Xo,options); toc %plot the results figure hold on plot(t,X(:,1));plot(t,X(:,2),':') legend('x1','x2');ylabel('x');xlabel('t') return %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [dx_dt]= TestFunction(t,x) %a function which returns a rate of change vector M = [-1,-1;... 1,-2] dx_dt = M*x; return
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
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M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
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M =
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M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
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M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
-1 -1
1 -2
M =
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1 -2
25 successful steps
0 failed attempts
151 function evaluations
Elapsed time is 0.723329 seconds.
