Please consider following ordinary differential equation system:
d(v)/dt=f0-f %f0 is constant ...... f,v are variables
d(v.c)/dt=f0-f.c-z % c,z are variables
d(z.v)/dt=z-f.c-v
if i want use ODE solver in Matlab, what is the format of writing differential equations?
You can use matlab symbolic to solve that system of equation. the code will be like A = dsolve ('equation') and go proceed sequentially. However, your system of equation will be resulted in the 2nd order ODE with variable coefficients in z. I don't think matlab can solve this since there's no general method to solve, unless you specify the resulted variable coefficients in the known forms.
Dear Mahdieh,
if you see attached link (first one), we have 3 equations and 3 variables but in your case you have 3 equations with 4 variables!!!!! I tried to solve your problem using Simulink (sketching on paper - like analogue computer) i found that I need the f variable. If you need the simulink file I can send it you tomorrow ( since I do not have MATLAB with me right now!!).
please see the attached files too, the last website just for further reading if you are interested!!
http://www3.nd.edu/~nancy/Math20750/Demos/3dplots/dim3system.html
https://www.mathworks.com/academia/student_center/tutorials/computational-math-tutorial-launchpad.html?confirmation_page
An example:
% Creating the MATLAB M-file containing the Lorenz equations.
function xprime= lorenz(t,x)
%values of parameters
I=1200;
k_f= 6.7*10.^7;
k_d= 6.03*10.^8;
k_n=2.92*10.^9;
k_p=4.94*10.^9;
lambda_b= 0.0087;
lambda_r =835;
gamma =2.74;
alpha =1.14437*10.^-3;
P_C= 3 * 10.^(11);
P_Q= 2.87 * 10.^(10);
% initial conditions
c=x(1);
s=x(2);
q=x(3);
%Non-linear differential equations.
% dc/dt= alpha*I*(1-c) + c*(- k_f - k_d - k_n * s - k_p*(1-q))
% ds/dt = lambda_b * c* P_C *(1-s)- lambda_r *(1-q)*s
% dq/dt = (1-q)* k_p * c *(P_C / P_Q)- gamma * q
xprime=[ alpha*I*(1-c) + c*(- k_f - k_d - k_n * s - k_p*(1-q)); lambda_b *(1-s)* c* P_C - lambda_r *(1-q)*s; (1-q)*k_p * c *(P_C / P_Q)- gamma * q];
Dear Mahdieh,
As I promised you , please see the attached file:
in your question you have 4 unknowns ( Variables) and 3 equations, I do not think there is a unique solution for that, i.e. you need to get/ find the 4th equation.
The Idea of Mohammad Mobashir be fine
for more information see the attach file
You can use numerical methods for system of ODEs like Runge Kutta method of order four if you need I cn send you the program or you can send me the system which you need to solve
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