ODE45, differential equation
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my function is
dy/dt=k*y*exp(450/y)
k is constant and y(0)=40 and y(15)=95 solve this equation by using ode45 can someone pleaseeeeeeeeeee check the code and make it work .
tspan = [0 300];
y0 = 40;y15=95
[t,y] = ode45(@(t,y) 'k'*y*exp(450/y), tspan, y0,y15);
plot(t,y,'-o')
采纳的回答
Hi,
if you search a value for k that complies with the boundary conditions, you could use fzero to solve the problem numerically:
k = fzero(@calculate_k, 0.001);
disp(['k = ', num2str(k)])
[t,y] = ode45(@(t,y) k*y*exp(450/y), [0 300], 40);
plot(t,y,'r')
hold on
scatter(15,95,'ob')
text(23,96,'y(t=15) = 95','Color','b')
hold off
function k_value = calculate_k(x)
tspan = [0 15];
y0 = 40;
[~,y] = ode45(@(t,y) x*y*exp(450/y), tspan, y0);
k_value = y(end) - 95;
end
This will give you as result:
k = 0.00010435
or if you need it more accurate:
k =
1.043495007807761e-04
and the plot which belongs to this result looks like the boundary conditions are met (To be precise, it keeps the boundary conditions. This is because fzero is a powerful tool and also because you can think of a very good initial value for x0 with just a few estimates...):
.
Best regards
Stephan
2 个评论
Takey Asaad
2018-9-17
No problem - please be patient with your questions. Dont ask the same question a second time, if it needs more time than you expected to get an answer.
Better try to give as much as and as good as possible informations that are needed to let the contributers give you a useful answer.
更多回答（3 个）
James Tursa
2018-9-15
0 个投票
Remove the quotes from 'k', and be sure to define k before you call ode45. Also, ode45 is an initial value problem solver, so the y15 variable is not applicable (remove it from the call).
9 个评论
Takey Asaad
2018-9-15
James Tursa
2018-9-15
Oh, I misunderstood. Since you are solving for k, this is not an initial value problem and ode45 is not the appropriate tool to use as I have outlined it. You might look at the boundary value problem link here:
And read the discussion following:
"The bvp4c solver can also find unknown parameters p for problems of the form ..."
Takey Asaad
2018-9-15
James Tursa
2018-9-15
You need to make an attempt at this. Look at the example involving an unknown parameter, and try to use that as an outline for your equation.
Takey Asaad
2018-9-15
James Tursa
2018-9-15
Please post your current code and let us know what specific problems you are having with it.
Takey Asaad
2018-9-15
编辑：James Tursa
2018-9-17
Takey Asaad
2018-9-15
编辑：James Tursa
2018-9-17
Takey Asaad
2018-9-15
编辑：James Tursa
2018-9-17
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