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Since I am using matlab ode23s solver, it contains two matlab files. One contains the differential equations and another contains plotting and to run the m-files. The code are working perfectly. Now I want to know the time step size that is using on the plot. How can i get the output of time step size. I would like to know the time step size that is using on the plot too. please help me.

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% 3 Nonlinear differential equations after Asymptotic expansion % with 1-c in dc/dt differential equation

function xpr= no(t,x)

  %values of parameters
    k_f= 6.7*10.^7;
    k_d= 6.03*10.^8; 
    k_n=2.92*10.^9; 
    k_p=4.94*10.^9;

    %Unknown parameters
    lambda_b= 0.0087;

    % scale parameters
    K_F= k_f * 10.^-9;
    K_D= k_d * 10.^-9; 
    K_N= k_n * 10.^-9; 
    K_P= k_p * 10.^-9;
    LAMBDA_B= lambda_b*10.^-9;

    %Pool Values
    P_C= 3 * 10.^(11);
    P_Q= 2.87 * 10.^(10); 

 % initial conditions
  c_0=x(1);
  s_0=x(2);
  q_0=x(3);

  %Non-linear differential equations.
  % dc_0/dtau=  c_0*(- K_F - K_D - K_N * s_0 - K_P*(1-q_0))
  % ds_0/dtau = Lambda_B * c* P_C *(1-s_0)
  % dq_0/dtau = (1-q_0)* K_P * c_0 *(P_C / P_Q)

xpr= zeros(3,1);

xpr(1)= c_0*(- K_F - K_D - K_N * s_0 - K_P*(1-q_0));
xpr(2)= LAMBDA_B * c_0* P_C *(1-s_0);
xpr(3)= (1-q_0)* K_P * c_0 *(P_C / P_Q);

xpr= [xpr(1);xpr(2);xpr(3)];

% TO RUN the 3 nonlinear differential equations after asymptotic expansion. % with 1-c in dc/dt differential equation

 format bank
  close all; 
  clear all; 
  clc; 

  %time interval
  ti=0; 
  tf=0.2; 
  tspan=[ti tf]; 

  x0=[0.25 0.02 0.98]; %initial conditions

  %time interval of [0 2] with initial condition vector [0.25 0.02 0.98] at time 0.
  options= odeset('RelTol',1e-4, 'AbsTol',[1e-4 1e-4 1e-4]);
  [t,x]= ode23s(@no,tspan,x0,options); 
  tDiffs = diff(t);   % to know time step size used in the plot

  %Plotting the graphs:
  figure 
  subplot(3,1,1), plot(t,x(:,1),'r'),grid on; 
  title('3 nonlinear differential equations (with 1-c)'),ylabel('c_0'); 

  subplot(3,1,2), plot(t,x(:,2),'b'),grid on; 
  ylabel('s_0'); 

  subplot(3,1,3), plot(t,x(:,3),'g'),grid on; 
  ylabel('q_0');xlabel('Time')

I have got the errors: Undefined function or variable 't'.

Manjushree
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  • What do you mean by time step size? Is it the step that it is using to plot the graph? For example, t=[1 2 3];x=[1 2 3];plot(t, x); % the step is 1. Please be more specific. – Kira Jul 15 '14 at 16:20
  • no, this is %time interval ti=0; tf=0.2; tspan=[ti tf]; but time stepsize is different. time step size is how many step size or grid point it has in time interval of between 0 and 1. – Manjushree Jul 16 '14 at 01:39

1 Answers1

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If I understand the question and the step size correctly:

The time step size can be specified in the command tspan=[ti:stepsize:tf].

So the t in [t, x] = ode23s(...) will be tspan. And if you do not specify any stepsize in your tspan then ode23s will make your t with the same size as your solution x.

Type help ode23s in MATLAB's command window and read the help provided. It can helps you.

Jika
  • 2,970
  • matlab didn't understand this code: tspan=[ti:stepsize:tf] – Manjushree Jul 17 '14 at 15:22
  • What does it say? Try tspan=ti:step:tf. For example tspan=0:0.01:0.2. – Jika Jul 17 '14 at 15:41
  • Tried tspan=ti:step:tf, but still i got errors, saying undefined variable of t. – Manjushree Jul 21 '14 at 19:47
  • Where did you use t in your code ? What value of time step do you want to use ? Give an example please because I do not have errors. – Jika Jul 21 '14 at 20:52
  • i have used t in this code: function xpr= no(t,x) – Manjushree Jul 24 '14 at 20:08
  • If you set the step size step=0.01 and you you set your vector tspan=0:step:0.2 and then you call your function xpr=no(t, x) specifying your vector x would work. Can you tell me the exact problem please? – Jika Jul 24 '14 at 20:34
  • Thank you for answer. I done that no errors now. can i ask u a question, why have you define step=0.01? isn't this ode23s need to find this out automatically. so can i look for it, whats the step size it is using? – Manjushree Jul 24 '14 at 21:06
  • I think it depends on the function x so the step size is automatically updated as the size of x. Maybe in the documentation of the ode23s function you can find the default values. – Jika Jul 24 '14 at 21:13
  • ya. without setting step=0.01, i want to know what step size ode23s is automatically updating? – Manjushree Jul 24 '14 at 21:42
  • Maybe if you see the vector x or t you can find out what are the step size. – Jika Jul 25 '14 at 02:02