# ODE45 is taking hours and hours to compute

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Bathala Teja
on 13 Sep 2021

Commented: Bathala Teja
on 14 Sep 2021

I want to solve 27 odes, for that i formed equations with matrices.

First i formed A(27*27 matrix), B(27*27 matrix) and C(25*25 matrix). All three are interms of 'theta'(i used 'sym' for forming A, B, C matrices). Now iam going to use these matrices to form ode eq's and solving using ode45.

Here i gave script after forming A, B, C matrices for some confidentiality.

% A, B, C matrices formed interms of theta

myfun = @(t,y)scriptname(t,y,A,B,C);

% dummy values for tspan and y0

tspan = [0 1];

y0 = zeros(27, 1);

% ode solver

sol = ode45(myfun,tspan,y0);

h = figure;

% plot

plot(sol.x,sol.y(i,:));

function dydt = scriptname(t,y,A,B,C)

Wr = 2*pi*50;

p =2;

% evaluation of C (numerical) with theta = y(27)

Cn = double(subs(C,y(27)));

for i=1:25

I(i,1)=y(i);

end

T1=1/2*p*I'*Cn*I

if t<0.5

T2=0;

else

T2=7.31;

end

V=[cos(Wr*t);

cos(Wr*t+2.*pi/3.);

cos(Wr*t-2.*pi/3.);

zeros(21, 1);

0;

(T1-T2);

y(26)]

% evaluation of A and B (numerical) with theta = y(27)

An = double(subs(A,y(27)));

Bn = double(subs(B,y(27)));

dydt = Bn\V-(An*y);

end

While running the script, it is taking hours and hours(i waited 5-6 hours and stopped compiling) but not giving any result.

I dont know what is wrong with the script.

Can anyone suggest me how to get result quickly.

##### 0 Comments

### Accepted Answer

Walter Roberson
on 14 Sep 2021

Pay attention to the fact that the if statement was removed from the code, and that instead the run was split into two pieces that pass in different T2 values. The mathematics used for ode45() is such that if you use two different branches of an if statement in a single call to ode45(), then there is a good chance that your code is wrong, and that you need to stop the integration at the boundary and then resume integration from where you left off.

% A, B, C matrices formed in terms of theta

commonvars = unique([symvar(A), symvar(B), symvar(C)]); %probably just theta

Afun = matlabFunction(A, 'vars', commonvars);

Bfun = matlabFunction(B, 'vars', commonvars);

Cfun = matlabFunction(C, 'vars', commonvars);

tspan1 = [0, 0.5]; T2_1 = 0;

tspan2 = [0.5, 1]; T2_2 = 7.31;

myfun1 = @(t,y)scriptname(t, y, T2_1, Afun, Bfun, Cfun);

myfun2 = @(t,y)scriptname(t, y, T2_2, Afun, Bfun, Cfun);

y0_1 = zeros(27, 1);

% ode solver

[t_1, y1] = ode45(myfun1, tspan1, y0_1);

y0_2 = y1(end,:);

[t_2, y2] = ode45(myfun2, tspan2, y0_2);

t = [t_1; t_2];

y = [y1; y2];

h = figure;

% plot

plot(t, y);

function dydt = scriptname(t, y, T2, Afun, Bfun, Cfun)

Wr = 2*pi*50;

p =2;

% evaluation of C (numerical) with theta = y(27)

Cn = Cfun(y(27));

for i=1:25

I(i,1)=y(i);

end

T1=1/2*p*I'*Cn*I

V=[cos(Wr*t);

cos(Wr*t+2.*pi/3.);

cos(Wr*t-2.*pi/3.);

zeros(21, 1);

0;

(T1-T2);

y(26)]

% evaluation of A and B (numerical) with theta = y(27)

An = Afun(y(27));

Bn = Bfun(y(27));

dydt = Bn\V-(An*y);

end

##### 5 Comments

Walter Roberson
on 14 Sep 2021

I have made a number of small changes to my working copy.

The code has a number of integral() operations that cannot be expected to have closed-form solutions, but MATLAB has to try to integral each of them when it sees int()

You can substitute in vpaintegral() and get through to the creation of the G, L, g matrices.

However at that point you want to matlabFunction() . But matlabFunction() does not support vpaintegral() .

In a recent release, MATLAB added a 'hold' option to int() to get an unevaluated int() form that you could manipuate and later release() . However... matlabFunction() does not handle the 'hold' option either.

You end up having to upgrade the vpaintegral() objects into int() objects. Sadly, that is very time consuming.

You have to understand some of the more obscure parts of the Symbolic Toolbox in order to upgrade the vpaintgral() into int() objects. But doing so is mostly a waste of time as you can predict that very few of the expressions will turn out to have closed form solutions, but upgrading to int() requires that MATLAB spend a lot of time trying to do the integration.

It might perhaps be easier to find all of the vpaintegral() calls and generate matlabFunction for the integrand, emit a wrapper function that does integral(), and then replace the vpaintegral() with a symoblic function reference... I am not sure at the moment that all this can be made to work.

### More Answers (1)

Jan
on 13 Sep 2021

Symbolic omputations need a lot of time. Can you implement the code numerically?

If the equation to be integrated is stiff, ODE45 tries to reduce the stepsize to mikroskopic values. Use a stiff solver in this case. e.g. ODE23S.

if t<0.5

Remember that Matlab's ODE integrators are designed to handle smooth functions only. Maybe this is a hard jump and the stepsize controller fails to pass this point. The correct way is to stop the integration at such jumps and restart it with the changed parameter.

##### 12 Comments

Jan
on 14 Sep 2021

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