how can I dissect a ode in 3 parts ! lets say I am starting from [0 t1] then stop the ode add a value to a parameter again start the ode[ t1 t2 ]then again change it back ?

sd()

Warning: RelTol has been increased to 2.22045e-14.

Warning: RelTol has been increased to 2.22045e-14.

%this is the code, lets say i dont add anything to the code then i should get back the original cycles
function sd
a = 0.021;
b = 0.025;
Dc = 100; % in microns
sigma = 1e1; % in MPa
mu_0 = 0.6;
Gmod = 3e4; % in MPa
v_shear = 3e9; % in microns/sec
rad = 0.5*Gmod/v_shear; % Radiation damping term
v_dyn = (a*sigma)/rad;
Kc = sigma*(b-a)/Dc; % in MPa/microns
v_init = 1e-2; % in microns/s
theta_init = Dc/v_init; % in seconds
tspan1=[0 2.5e7];
solopt = odeset('RelTol',1e-16);
t_step = 1e5; % in seconds
Im_stiff_osc = sigma*(sqrt(b)-sqrt(a))^2/Dc;
rat_oscillatory_sol = Im_stiff_osc/Kc;
stiff = 0.7*Im_stiff_osc; % Stiffness 
B_s=mu_0*sigma;
law = 'A';
par = [a,b,Dc,sigma,stiff,rad];
taudot_step=[0 9*10e-9*B_s 2.6*10e-9*B_s];
[t1,y11] = ode45(@(t,y)ode5(t,y,par,v_init,t_step,law),...
    tspan1,[theta_init;v_init],solopt);
theta_init=y11(end,1);
v_init=y11(end,2);
tspan2=tspan1+2.51e7;
[t2,y12]=ode45(@(t,y)ode5(t,y,par,v_init,t_step,law),...
    tspan2,[theta_init;v_init],solopt);
figure()
semilogy(t1,y11(:,2),'r')
hold on
semilogy(t2,y12(:,2),'g')
ylabel ('$velocity$', 'Interpreter','latex')
xlabel ('time[s]')
hold off  
end
function dydt = ode5(t,y,par,v_lp,t_step,law) 
aa = par(1); bb = par(2); dc = par(3); sigma = par(4); stiff = par(5);
rad = par(6);
dydt = zeros(2,1);
omega = y(1)*y(2)/dc;
dydt(1) = 1.d0 - omega; 
if t <= t_step
    v_loc = v_lp;
elseif t > t_step
    v_loc=1.000001*v_lp;
else
    v_loc = 1.00000*v_lp;
end
tau_dot  = stiff*(v_loc- y(2));
if strcmp(law,'A')
    dydt(1) = 1.d0 - omega;
elseif strcmp(law,'S')
    dydt(1) = -omega*log(omega);
end
dydt(2) = ((tau_dot/sigma - bb*dydt(1)/y(1)))/(aa/y(2)+rad/sigma);
end

[SOUVIK DARIPA]

@Torsten can i use odextend to achieve the above.

[Torsten]

I don't understand why you stop integration after tspan1 and restart the solver because you don't change any parameter in your ODE as you claimed in the title.

[SOUVIK DARIPA]

I will, but first I have to ensure that I am getting back the same cycle Without adding anything else.

[Torsten]

Yes, of course you will get the same plot if you don't change anything in the equations. But there seem to be singularities in your solution function.