Matlab, how to know time step size in the plot or how can i get the output of time step size?

Since i am using matlab ode23s solver, it contains two matlab files . One contain 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.

=>

% 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);

        %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')

Answer 1

[Geoff Hayes]

Just after your code executes

 [t,x]= ode23s(@no,tspan,x0,options);

add

 tDiffs = diff(t);

which will return the difference between adjacent elements in t...which should correspond to the time step sizes used in the plots (as t is used in each plot call).

[dave]

I have added this code,

tDiffs = diff(t);

and i can see the numbers of time step size coming as output. now to plot it what can i do for three graphs?

[Geoff Hayes]

Are you sure that the code is in this order

 [t,x]= ode23s(@no,tspan,x0,options); 
 tDiffs = diff(t);

[dave]

yes. the code is in this order

[t,x]= ode23s(@no,tspan,x0,options); 
 tDiffs = diff(t);

Now how can i see the time step size it is using in the plot?

[Geoff Hayes]

Look at tDiffs - it will be the difference between adjacent elements, and this difference should be the time step size. Are each of the values in tDiffs identical?