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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.

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

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.

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