How do I solve these differential equations using a while loop?
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1 个评论
Roger Stafford
2018-3-11
编辑：Roger Stafford
2018-3-11
If you want to allow delta t to approach zero as a limit, you can solve these equations using one of the ode functions. The first equation, for example, would have the form:
dU/dt = k1-k2*X./((X.^2+Y.^2+Z.^2).^(3/2))
On the other hand if you wish to solve them using delta t as a fixed nonzero value, then do so with a for-loop to provide the iteration, not a while-loop. Just carry out the operations you have given here within the for-loop at each step going from the n-th values to the n+1-st values.
采纳的回答
Abraham Boayue
2018-3-12
i = 1;
while i <= n-2
i = i +1;
% write all your code
% here. This will produce
% the same results as the
% for loop.
end
1 个评论
Abraham Boayue
2018-3-12
You change the for loop to the while loop above, it does the same operation as the for loop.
更多回答（1 个）
Abraham Boayue
2018-3-12
clear variables
close all
% Define parameters
dt = dt;
t = t0:dt:tf;
n = length(t);
m = m;
thx = thx;
thy = thy;
thz = thz;
G = G;
Me = Me;
% Initializations Initial conditions Boundary conditions
u = zeros(1,n); u(1) = u0; u(n) = un;
v = u; v(1) = v0; v (n)= vn;
w = v; w(1) = w0; w(n) = wn;
x = w; x(1) = x0; x(n) = xn;
y = x; y(1) = y0; y(n) = yn;
z = y; z(1) = z0; z(n) = zn;
for i = 2: n-1
u(i+1) = u(i) + (thx/m - G*Me*(x(i)/(x(i)^2 +y(i)^2 +z(i)^2)^(3/2)))*dt;
v(i+1) = v(i) + (thy/m - G*Me*(y(i)/(x(i)^2 +y(i)^2 +z(i)^2)^(3/2)))*dt;
w(i+1) = w(i) + (thz/m - G*Me*(z(i)/(x(i)^2 +y(i)^2 +z(i)^2)^(3/2)))*dt;
x(i) = x(i) + u(i+1)*dt;
y(i) = y(i) + v(i+1)*dt;
z(i) = z(i) + w(i+1)*dt;
end
figure;
plot(t,u,'linewidth',2);
hold on
plot(t,v,'linewidth',2);
plot(t,w,'linewidth',2);
plot(t,x,'linewidth',2);
plot(t,y,'linewidth',2);
plot(t,z,'linewidth',2);
a = ylabel('Pressure');
set(a,'Fontsize',14);
a = xlabel('x');
set(a,'Fontsize',14);
a=title(['Solution to system of ode - dt = ' num2str(dt)]);
legend('u', 'v','w','x','y','z')
xlim([0 1]);
set(a,'Fontsize',16);
grid;
5 个评论
Abraham Boayue
2018-3-12
Hey Christopher Here is a model solution to your equations. I could not test the code since you did not provide any parameter. The coding was straight forward using a for loop as Roger suggested. I hope this will help you get started with your coding. Best of lucks!
Christopher Maraj
2018-3-12
Abraham Boayue
2018-3-12
Hey Chris, what are these equations by the way? Do you have access to the actual differential equations? Can you post the values of the parameters as well as the initial and boundary conditions? I would like to see what they represent by running the code.
Christopher Maraj
2018-3-12
yes sure, here they are:
Christopher Maraj
2018-3-12
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