How to use ode15s to solve a stiff ode with mass?

2 次查看（过去 30 天）
Deyun
Deyun 2024-4-22
评论： Deyun 2024-4-24
Now I get a matlab code using ode15s to solve a function with singular Mass. My question is:
what does it mean (there is no function called 'M' in my dir)
opts = odeset('Mass', 'M', 'MassSingular', 'yes');
and why in the ode function, there is an extra input called 'flag' ?
The main code is as following:
tf = 200;
x0 = [0 0 0 0 2500 0 0.8 0 50 50 50 50 5];
opts = odeset('Mass', 'M', 'MassSingular', 'yes');
[t, x] = ode15s('ff', [0 tf], x0,opts);
function xdot=Methanol_Water(t,x)
if isempty(flag),
P=1;
x1=x(1);
x2=x(2);
x3=x(3);
x4=x(4);
x0=x(6);
xB=x(7);
T1=x(9);
T2=x(10);
T3=x(11);
T4=x(12);
TB=x(13);
D1=-4617.8;
C1=13.676;
D2=-5042.6;
C2=13.519;
A=0.85;
B=0.48;
R=10;
V=10;
Di=V/(R+1);
L=V-Di;
y1=exp(A*(1-x1^2)/(1-x1+A*x1/B)^2)*exp(C1+D1/(273.15+T1))*x1/P;
y2=exp(A*(1-x2^2)/(1-x2+A*x2/B)^2)*exp(C1+D1/(273.15+T2))*x2/P;
y3=exp(A*(1-x3^2)/(1-x3+A*x3/B)^2)*exp(C1+D1/(273.15+T3))*x3/P;
y4=exp(A*(1-x4^2)/(1-x4+A*x4/B)^2)*exp(C1+D1/(273.15+T4))*x4/P;
yB=exp(A*(1-xB^2)/(1-xB+A*xB/B)^2)*exp(C1+D1/(273.15+TB))*xB/P;
MH0=100;
MH=20;
xdot(1)=1/MH*(L*(x0-x1)+V*(y2-y1));
xdot(2)=1/MH*(L*(x1-x2)+V*(y3-y2));
xdot(3)=1/MH*(L*(x2-x3)+V*(y4-y3));
xdot(4)=1/MH*(L*(x3-x4)+V*(yB-y4));
xdot(5)=L-V;
xdot(6)=(V/MH0*y1-(L+Di)/MH0*x0);
xdot(7)=(L*(x4-xB)-V*(yB-xB));
xdot(8)=Di;
xdot(9)=P-exp(A*(1-x1^2)/(1-x1+A*x1/B)^2)*exp(C1+D1/(273.15+T1))*x1-exp(A*x1^2/(x1+A*(1-x1)/B)^2)*exp(C2+D2/(273.15+T1))*(1-x1);
xdot(10)=P-exp(A*(1-x2^2)/(1-x2+A*x2/B)^2)*exp(C1+D1/(273.15+T2))*x2- exp(A*x2^2/(x2+A*(1-x2)/B)^2)*exp(C2+D2/(273.15+T2))*(1-x2);
xdot(11)=P-exp(A*(1-x3^2)/(1-x3+A*x3/B)^2)*exp(C1+D1/(273.15+T3))*x3-exp(A*x3^2/(x3+A*(1-x3)/B)^2)*exp(C2+D2/(273.15+T3))*(1-x3);
xdot(12)=P-exp(A*(1-x4^2)/(1-x4+A*x4/B)^2)*exp(C1+D1/(273.15+T4))*x4- exp(A*x4^2/(x4+A*(1-x4)/B)^2)*exp(C2+D2/(273.15+T4))*(1-x4);
xdot(13)=P-exp(A*(1-xB^2)/(1-xB+A*xB/B)^2)*exp(C1+D1/(273.15+TB))*xB- exp(A*xB^2/(xB+A*(1-xB)/B)^2)*exp(C2+D2/(273.15+TB))*(1-xB);
xdot = xdot(:);
else
M = zeros(13,13);
M(1,1) = 1;
M(2,2) = 1;
M(3,3) = 1;
M(4,4) = 1;
M(5,5) = 1;
M(6,6) = 1;
M(7,7) = x(5);
M(8,8) = 1;
xdot = M;
end
  1 个评论
Aquatris
Aquatris 2024-4-22
Something does not feel right.
  • you call ode15s with 'ff' argument, I do not think this is right way to call it
  • The Methanol_Water function returns xdot as 13 element vector if 'flag', and if not it is an 8x8 matrix, which is not a regular ODE problem.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Torsten
Torsten 2024-4-22
编辑：Torsten 2024-4-22
Ran in:
tf = 200;
x0 = [0 0 0 0 2500 0 0.8 0 50 50 50 50 5];
M = zeros(13,13);
M(1,1) = 1;
M(2,2) = 1;
M(3,3) = 1;
M(4,4) = 1;
M(5,5) = 1;
M(6,6) = 1;
%M(7,7) = x(5); % changed and divided xdot(7) by x(5) instead.
M(7,7) = 1;
M(8,8) = 1;
opts = odeset('Mass', M, 'MassSingular', 'yes');
[t, x] = ode15s(@Methanol_Water, [0 tf], x0,opts);
plot(t,x)
function xdot=Methanol_Water(t,x)
P=1;
x1=x(1);
x2=x(2);
x3=x(3);
x4=x(4);
x0=x(6);
xB=x(7);
T1=x(9);
T2=x(10);
T3=x(11);
T4=x(12);
TB=x(13);
D1=-4617.8;
C1=13.676;
D2=-5042.6;
C2=13.519;
A=0.85;
B=0.48;
R=10;
V=10;
Di=V/(R+1);
L=V-Di;
y1=exp(A*(1-x1^2)/(1-x1+A*x1/B)^2)*exp(C1+D1/(273.15+T1))*x1/P;
y2=exp(A*(1-x2^2)/(1-x2+A*x2/B)^2)*exp(C1+D1/(273.15+T2))*x2/P;
y3=exp(A*(1-x3^2)/(1-x3+A*x3/B)^2)*exp(C1+D1/(273.15+T3))*x3/P;
y4=exp(A*(1-x4^2)/(1-x4+A*x4/B)^2)*exp(C1+D1/(273.15+T4))*x4/P;
yB=exp(A*(1-xB^2)/(1-xB+A*xB/B)^2)*exp(C1+D1/(273.15+TB))*xB/P;
MH0=100;
MH=20;
xdot(1)=1/MH*(L*(x0-x1)+V*(y2-y1));
xdot(2)=1/MH*(L*(x1-x2)+V*(y3-y2));
xdot(3)=1/MH*(L*(x2-x3)+V*(y4-y3));
xdot(4)=1/MH*(L*(x3-x4)+V*(yB-y4));
xdot(5)=L-V;
xdot(6)=(V/MH0*y1-(L+Di)/MH0*x0);
%xdot(7)=(L*(x4-xB)-V*(yB-xB)); % Divided by M(7,7) = x(5) instead
xdot(7)=(L*(x4-xB)-V*(yB-xB))/x(5);
xdot(8)=Di;
xdot(9)=P-exp(A*(1-x1^2)/(1-x1+A*x1/B)^2)*exp(C1+D1/(273.15+T1))*x1-exp(A*x1^2/(x1+A*(1-x1)/B)^2)*exp(C2+D2/(273.15+T1))*(1-x1);
xdot(10)=P-exp(A*(1-x2^2)/(1-x2+A*x2/B)^2)*exp(C1+D1/(273.15+T2))*x2- exp(A*x2^2/(x2+A*(1-x2)/B)^2)*exp(C2+D2/(273.15+T2))*(1-x2);
xdot(11)=P-exp(A*(1-x3^2)/(1-x3+A*x3/B)^2)*exp(C1+D1/(273.15+T3))*x3-exp(A*x3^2/(x3+A*(1-x3)/B)^2)*exp(C2+D2/(273.15+T3))*(1-x3);
xdot(12)=P-exp(A*(1-x4^2)/(1-x4+A*x4/B)^2)*exp(C1+D1/(273.15+T4))*x4- exp(A*x4^2/(x4+A*(1-x4)/B)^2)*exp(C2+D2/(273.15+T4))*(1-x4);
xdot(13)=P-exp(A*(1-xB^2)/(1-xB+A*xB/B)^2)*exp(C1+D1/(273.15+TB))*xB- exp(A*xB^2/(xB+A*(1-xB)/B)^2)*exp(C2+D2/(273.15+TB))*(1-xB);
xdot = xdot(:);
end

类别

在 Help Center 和 File Exchange 中查找有关 Ordinary Differential Equations 的更多信息

标签

产品


版本

R2021b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by