Need help with solving differential equation using multiple initial values!

Question

Adel Naqvi 2016-11-19

0
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https://ww2.mathworks.cn/matlabcentral/answers/313044-need-help-with-solving-differential-equation-using-multiple-initial-values

编辑： Walter Roberson 2016-11-21

Hello!

I am to solve a differential equation for a school project, and am to plot a solution curve given an intial angle and depth.

I wrote the following:

        function dZ=trace(~,Z)
        p = [5.6596 14.5820 257.4318];
        c=@(z) 4800+p(1)+((p(2))*z/1000)+((p(3))*exp(-z/1000)); % c(z)
        c=c(2000);
% inital conditions are given by: Z(1), the speed, and Z(2), the angle. 
      dZ=zeros(2,1); 
      dZ(1)=Z(2);
  n=7.8;
  q0=(c/cosd(n))^2;
      dZ(2)=-q0*(((-p(3)/1000)*exp(-Z(1)/1000))+p(2)/1000)/((4800+p(1)+(p(2)*Z(1)/1000)+(p(3)*exp(-Z(1)/1000))^3));
  end

The above is my function file for solving a second order ODE, who I then call using the following:

[X,Z]=ode45(@trace,[0:6076*25],[2000 tand(7.8)]); %solves the differential equation.
plot(X(151700:end),Z(151700:end,1),'-r') %plots a solution curve for z(x)

My problem then arises when I am to solve for multiple values of n, i.e, for angles ranging between -10-14 degrees. I could change my function 'trace' to take another input 'n', which I then specify in my other script (maybe by way of a for-loop?), but the ode45 solver does to accept this additional parameter. Also, this would mean slightly different values for the variable 'q0' each time I have a different n, and it being a part of the ODE, means slightly different diff equations for me to solve.

How to I change my code to accommodate this additional issue? Any insight/tips would be much appreciated!