How to solve system of first order ODE's by forming matrix

조회 수: 4(최근 30일)
Bathala Teja 2021년 8월 30일
댓글: Bathala Teja 2021년 8월 31일
Q:
dy1/dt = 2*y1+5*y2+y3
dy2/dt = 7*y1+9*y2
dy3/dt = 4*y1+y2+3*y3
y1(0) = 0, y2(0)= 0, y3(0) = 0;
i want to plot y1(t), y2(t) and y3(t) waveforms over time 0 to 10sec.
i tried the below code
syms y1(t) y2(t) y3(t)
Y = [y1(t);
y2(t);
y3(t)];
A = [2 5 1;
7 9 0;
4 1 3];
diff(Y, t) = A.*Y;
tspan = [0 10];
Y(0)=zeros(1.,3);
[t, Y] = dsolve(diff(Y, t), tspan, Y(0));
Y1 = Y(:, 1);
plot(t, Y1);
Y2 = Y(:, 1);
plot(t, Y2);
Y3 = Y(:, 1);
plot(t, Y3);
But iam getting an error like this
>> Untitled5
Error using sym/subsindex (line 864)
Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be
symbolic variables, and function body must be sym expression.
Error in sym/privsubsasgn (line 1151)
L_tilde2 = builtin('subsasgn',L_tilde,struct('type','()','subs',{varargin}),R_tilde);
Error in sym/subsasgn (line 972)
C = privsubsasgn(L,R,inds{:});
Error in Untitled5 (line 9)
diff(Y, t) = A.*Y;
Anyone please tell where i went wrong. I want to solve with matrices(since my main code have 20 ODE's to solve) only, please suggest me in this way only.

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채택된 답변

Wan Ji 2021년 8월 30일
편집: Wan Ji 2021년 8월 30일
Do not use syms, because without syms, the code runs faster
A = [2 5 1;
7 9 0;
4 1 3];
odefun = @(t,Y)A*Y;
tspan = [0 10];
Y0=zeros(3,1);
[t, Y] = ode45(odefun, tspan, Y0);
Y1 = Y(:, 1);
hold on
plot(t, Y1);
Y2 = Y(:, 1);
plot(t, Y2);
Y3 = Y(:, 1);
plot(t, Y3);
legend('Y1','Y2','Y3') As the initial conditions are all zero, the final results become zero for Y1 Y2 and Y3
IF you want to use syms
syms y1(t) y2(t) y3(t)
A = [2,5,1;7,9,0;4,1,3];
eq = diff([y1;y2;y3])==A*[y1;y2;y3];
conds = [y1(0)==0; y2(0)==0; y3(0)==0];
[y1,y2,y3] = dsolve(eq,conds)
tspan = 0:0.1:10;
y_1 = eval(subs(y1,t,tspan));
y_2 = eval(subs(y2,t,tspan));
y_3 = eval(subs(y3,t,tspan));
figure(1)
clf
hold on
plot(tspan, y_1);
plot(tspan, y_2);
plot(tspan, y_3);
legend('Y1','Y2','Y3')
Then the result becomes
y1 =
0
y2 =
0
y3 =
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Bathala Teja 2021년 8월 31일
if you dont mind can you tell me how to form a variable array without using symbolic math toolbox.
Nr = 20
nr = rand(1, Nr)
p =2;
Nr = 20
for j = 1:(2*p)
for n = (((j-1)*Nr/(2*p))+2):(j*(Nr/(2*p)))
Aord = 1/(2*pi);
nr(1, n) = nr(1, n)+cos((phi-theta-((n-j-1)*2)-((j-1)*2)))+Aord;
end
end
Here nr is a array of Nr elements consists of theta and phi in it. How to form without using sym.

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추가 답변(1개)

Bathala Teja 2021년 8월 30일
Firstly iam very happy for your suggestion, thank you very much.
First solution is fine. But i have some complexity in my main code.
My main code contains contains A and B matrices(both 3*3) and is interms of some variable teta.
I want to substitute y3 in place of teta and proceed solving ODE's.
My ODE is inv(B).*(V-(A*Y)), where V = column matrix of order 3.
i tried like this
syms teta
Ai = cos(teta).*([2 5 1;
7 9 0;
4 1 3])
Bi = sin(teta).*([1 2 3;
4 5 6;
7 8 9])
V = ones(3, 1)
odefun = @(t,Y) inv(B).*(V-(A*Y));
A = subs(Ai, teta, Y(3))
B = subs(Bi, teta, Y(3))
tspan = [0 10];
Y0=zeros(3,1);
[t, Y] = ode45(odefun, tspan, Y0);
Y1 = Y(:, 1);
hold on
plot(t, Y1);
Y2 = Y(:, 1);
plot(t, Y2);
Y3 = Y(:, 1);
plot(t, Y3);
legend('Y1','Y2','Y3')
But iam getting this error
Unrecognized function or variable 'Y'.
Error in Untitled5 (line 43)
A = subs(Ai, teta, Y(3))
Problem is with substitute Y3, how to resolve that?
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Bathala Teja 2021년 8월 30일

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