Differential equation ode45 matlab

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Alex7210
Alex7210 2014-8-27
编辑： Star Strider 2014-8-28
Hi! I have a differential equation and I try to solve them by Matlab (ODE45) For example:
function dy = f8(t,y)
dy = 3 - 3./25.*y; %(1)
tspan = [0, 2]; y0 = -3;
[Y,T] = ode45(@f8, tspan, y0);
plot(Y,T)
grid on
When the curve reaches=0, I have to go to the equation of (2):
dy = 10-3./10.*y; %(2)
Please, help me, How can I do it?

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回答（1 个）

Star Strider
Star Strider 2014-8-27
You need to detect the zero-crossing as an ‘event’. See the documentation on Event Location for details.
It is not difficult, but it can be a bit of a challenge to get it working the first time you do it.
  2 个评论
Alex7210
Alex7210 2014-8-28
Thanks for your answer! I could detect zero-crossing.
tspan = [0, 10]; x0 = -3;
options = odeset('Events', @kg15);
[t,x,te,xe,ie] = ode45(@f8, tspan, x0, options);
plot(t,x); grid on
%==============================
function dy = f8(t,y)
dy = 3-3./25.*y;
%==============================
function [value, isterminal, ...
direction] = kg15(t,x)
value = x-0;
isterminal = 1;
direction = 1;
But how can I continue my second equation? Help me please to understand it
Star Strider
Star Strider 2014-8-28
编辑：Star Strider 2014-8-28
First, when the integration stops at the zero-crossing, immediately store your first set of t and x values as an array so they do not get overwritten.
Second, use the last t and x values for your new initial t and x values, call ode45 with your second function and those initial conditions and time, and continue integrating until the end of tspan.
Third, append your second set of t and x values to your first set to get the complete integration sequence. (It does not appear from your second ODE that you will have another zero-crossing, so you will only have to do this once.)

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