How do I solve these differential equations using a while loop?

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Christopher Maraj 2018-3-11

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https://ww2.mathworks.cn/matlabcentral/answers/387559-how-do-i-solve-these-differential-equations-using-a-while-loop

评论： Christopher Maraj 2018-3-12

采纳的回答： Abraham Boayue

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Roger Stafford 2018-3-11

编辑：Roger Stafford 2018-3-11

在 MATLAB Online 中打开

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.

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Answer 1

Abraham Boayue 2018-3-12

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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

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Abraham Boayue 2018-3-12

You change the for loop to the while loop above, it does the same operation as the for loop.

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Answer 2

Abraham Boayue 2018-3-12

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在 MATLAB Online 中打开

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;