Why do I receive this error msg when solving a simple DAE with odefunction?

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Hainan Wang 2021-6-9

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评论： Hainan Wang 2021-6-20

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When I solve this simple DAE with three variables y1(t), y2(t), y3(t),

y1' = y2' + y1;

y2' = y1;

y3 = y1 + y2;

y1(0) = 1.0;

y2(0) = 0.5;

y3(0) = 1.5;

syms y1(t) y2(t) y3(t)
eqs = [diff(y1(t),t) == diff(y2(t),t) +  y1(t),...
       diff(y2(t),t) == y1(t),...
       y3(t) == y1(t) + y2(t)];
vars = [y1(t) y2(t) y3(t)];
initConditions = [1 0.5 1.5];
[M,F] = massMatrixForm(eqs,vars);
M = odeFunction(M,vars);
F = odeFunction(F,vars);
opt = odeset('mass',M);
ode15s(F, [0 1], initConditions, opt)

I receive this error msg:

Need a better guess y0 for consistent initial conditions.

This DAE is simple, if subs y2' = y1 into first equation, then y1' = 2y1. With y1(0) = 1, y2(0) = 0.5, can solve y1 = e^2t and y2 = e^2t/2. And y3(0) = y1(0)+y2(0)=1.5. What's wrong with my guess on initial condition, most likely for y3?

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Answer 1

Harshitha Kallam 2021-6-15

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Yes, the most likely reason for error is the initial value of y3 that is resulting in inconsistency.

A possible workaround can be to first solve for y1(t), y2(t) and then calculate y3(t) which is a summation of those two. Alternatively, the below modification can be done.

eqs = [diff(y1(t),t) == diff(y2(t),t) +  y1(t),...
       diff(y2(t),t) == y1(t),...
       diff(y3(t),t) == diff(y1(t) + y2(t),t)]; %changing the last eqn

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Hainan Wang 2021-6-20

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Thank you for your response!

However, I figure out that I can solve it with below code while keeping the 3rd equation as y3(t)=y1(t)+y2(t).

M = [1 -1 0; 0 1 0; 0 0 0];
optODE = odeset('Mass', M);
initConditions = [1 0.5 1.5]';
ode15s(@(t,y)dyneqn(t,y), [0 1], initConditions, optODE)
function dydt = dyneqn(t,y)
dydt = zeros(3,1);
dydt(1) = y(1);
dydt(2) = y(1);
dydt(3) = y(1) + y(2) - y(3);
end 