numerical methods - Using ode45 in Matlab -


i'm trying simulate time behavior physical process governed system of odes. when switch width of input pulse 20 19, there no depletion of y(1) state, doesn't make sense physically. doing wrong? using ode45 incorrectly?

function test  width = 20; center = 100;  tspan = 0:0.1:center+50*(width/2);  [t,y] = ode45(@odesystem,tspan,[1 0 0 0]);  plot(t,y(:,1),'k*',t,y(:,2),'k:',t,y(:,3),'k--',t,y(:,4),'k'); hold on; axis([center-3*(width/2) center+50*(width/2) -0.1 1.1]) xlabel('time') ylabel('relative values') legend({'y1','y2','y3','y4'});      function dy = odesystem(t,y)         k1 = 0.1;         k2 = 0.000333;         k3 = 0.1;          dy = zeros(size(y));          % rectangular pulse         = rectpuls(t-center,width);          % ode system         dy(1) = -k1*i*y(1);         dy(2) = k1*i*y(1) - k2*y(2);         dy(3) = k2*y(2) - k3*i*y(3);         dy(4) = k3*i*y(3);     end end

you changing parameters of your odes discontinuously in time. results in stiff system , less accurate, or wrong, results. in case, because ode simple when i = 0, adaptive solver ode45 take large steps. thus, there's high probability step right on region inject impulse , never see it. see my answer here if you're confused why code in question misses pulse though you've specified tspan have (output) steps of 0.1.

in general bad idea have discontinuities (if statements, abs, min/max, functions rectpuls, etc.) in integration function. instead, need break integration , calculate results piecewise in time. here's modified version of code implements this:

function test_fixed  width = 19; center = 100;  t = 0:0.1:center+50*(width/2); = rectpuls(t-center,width); % removed ode function, kept if wanted plotting  % before pulse tspan = t(t<=center-width/2); y0 = [1 0 0 0]; [~,out] = ode45(@(t,y)odesystem(t,y,0),tspan,y0); % t pre-calculated, no need return y = out;  % pulse tspan = t(t>=center-width/2&t<=center+width/2); y0 = out(end,:); % initial conditions same last stage previous integration [~,out] = ode45(@(t,y)odesystem(t,y,1),tspan,y0); y = [y;out(2:end,:)]; % append new data removing identical initial condition  % after pulse tspan = t(t>=center+width/2); y0 = out(end,:); [~,out] = ode45(@(t,y)odesystem(t,y,0),tspan,y0); y = [y;out(2:end,:)];  plot(t,y(:,1),'k*',t,y(:,2),'k:',t,y(:,3),'k--',t,y(:,4),'k'); hold on; axis([center-3*(width/2) center+50*(width/2) -0.1 1.1]) xlabel('time') ylabel('relative values') legend({'y1','y2','y3','y4'});      function dy = odesystem(t,y,i)         k1 = 0.1;         k2 = 0.000333;         k3 = 0.1;          dy = zeros(size(y));          % ode system         dy(1) = -k1*i*y(1);         dy(2) = k1*i*y(1) - k2*y(2);         dy(3) = k2*y(2) - k3*i*y(3);         dy(4) = k3*i*y(3);     end end

see my answer similar question.


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