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Solving Non-linear System of 3 diff eqns using ode23s in matlab

  1. Jun 20, 2014 #1

    wel

    User Avatar
    Gold Member

    I am trying to solve 3 differentail equations(Lorenz equations) using ode solver: ode23s in Matlab. Here are the 3 lorenz 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

    I have used the ode solver and created two M-files ode.m and lorenz.m

    => Here are my two Matlab M-files. This is my 1st M-file : ode.m which i ran to plot the graph.
    Code (Text):

          format bank
          close all;
          clear all;
          clc;
         
          %time interval
          ti=0;
          tf=140;
          tspan=[ti tf];
         
          x0=[0.25 0.02 0.98]; %initial vectors
         
          %time interval of [0 2] with initial condition vector [0.25 0.02 0.02] at time 0.
          options= odeset('RelTol',1e-4, 'AbsTol',[1e-4 1e-4 1e-4]);
          [t,x]= ode23s('lorenz',tspan,x0,options);
         
          %Plotting the graphs:
          figure
          subplot(3,1,1), plot(t,x(:,1),'r'),grid on;
          title('Lorenz Equations'),ylabel('c');
         
          subplot(3,1,2), plot(t,x(:,2),'b'),grid on;
          ylabel('s');
         
          subplot(3,1,3), plot(t,x(:,3),'g'),grid on;
          ylabel('q');xlabel('t')

    This is my second M-file which is lorenz.m

    Code (Text):
          % 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];
    Please help me, both M-files codes are working but i want to use function handle (@lorenz) in lorenz.m file because Lorenz isn’t very descriptive of this problem. And also, when i run ode.m file , the values of plot are really small but when i run the lorenz.m file , the values of c,s,q are really big.I want to get values of s and q somewhere between 0 to 1. And value of c should be really big number something 3.5 X10^11. I don't know what is going on?
     
  2. jcsd
  3. Jul 2, 2014 #2
    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
     
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