MATLAB: Running the code takes too long to finish(Euler’s Method)

differential equations

I'm trying to create a code to use Euler's method in solving the differential equation as shown below. When I try to run the code, it takes a long time to do each iteration. I feel I have made a mistake when declaring variables. I have also placed a picture of a segment of the supposed output of the code which I got from my professor. Any insight would be appreciated.

rho=1000;

g=9.8;

A_tank=3.13;

A_pipe=0.06;

C=pi/12;

K1=300;

K2=1000;

syms dh(t,h)

dh(t,h)=(K1+K2*sin(5*C*t)*cos(C*t)-rho*A_pipe*(2*g*h)^(1/2))/(rho*A_tank);

t=0;

tn=150;

h=3;

s=0.1;

ts=t:s:tn;

hwt=[];

fprintf('time \t\t height \n')

fprintf('%f \t %f\t \n',t,h)

for i=1:numel(ts)

h=h+dh(t,h)*s;

t=t+s;

fprintf('%f \t %f\t \n',t,h);

hwt(i)=h;

end

plot(ts,hwt)

Best Answer

Remove

syms dh(t,h)

and replace

dh(t,h)=(K1+K2*sin(5*C*t)*cos(C*t)-rho*A_pipe*(2*g*h)^(1/2))/(rho*A_tank);

with

dh = @(t,h)(K1+K2*sin(5*C*t)*cos(C*t)-rho*A_pipe*(2*g*h)^(1/2))/(rho*A_tank);

to get

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Some comments

1) Q is defined twice as symbolic variable, but it is actually an array

2) in the first loop N = 4, so length(t) = 4 and length(E1) = 4; [btw: the real length is 5 because i = 1 is not addressed: your index is always i+1]. In the second loop N = 40, so length(t) = 40 and length(E2) = 40. In the end you use the same t for plottin either E1 and E2.

My suggestion is to use different vectors for the first and second loop, maybe t1 and t2. Then preallocate always your vectors. Finally in the loop, address Q(i) and E1(i) (and E2) instead of Q(i+1) and E1(i+1)

Best Answer

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