Find relation of initial value and maximum of the value by solving this odes

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嘉杰 程
嘉杰 程 2021년 10월 19일
편집: 嘉杰 程 2021년 10월 19일
by solving this ode, we could get the relation plot of r and m (assuming =2,=0),
now I want to change the value of (between 0-4) to get maximum of munder each , and I also want to plot , could anyone help me? thank you!
basic code between m-r like this:
fun2.m
function dtm=func2(r,tm)
dtm=zeros(2,1);
dtm(1)=(-4)*(sinh(tm(1))-2*sinh(tm(1)/2))*(r^3*(sinh(tm(1)) ...
-8*sinh(tm(1)/2)+3*tm(1))+tm(2))/((3*tm(1))*(tm(1)-2*tm(2))* ...
(cosh(tm(1))-4*sinh(tm(1)/2)+3));
dtm(2)=(r^2)*(sinh(tm(1))-tm(1));
and here is the main.m
rspan=[0 20];
y0=[2;0];
[r,y]=ode45(@func2,rspan,y0);
subplot(1,2,1)
plot(r,y(:,2),'b-');
M=max(y(:,2));
grid on;
title('m-r');
axis([0 4 0 2])
xlabel('r'); ylabel('m');
legend('y_1','y_2')
subplot(1,2,2)

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