# Is it possible to get a time-dependent function as an output of an ODE solver?

1 view (last 30 days)
Nang Su Lwin on 23 Nov 2022
Answered: Steven Lord on 24 Nov 2022
My code is below, it plots as I expect it to. I would like to know if it is possible to get an output where the ODE solver gives the solution as a function in time rather than 2 column vectors [T,Y]. I wanted to use the output to further analyze something, but need a function in time rather than the column vectors.
clear all
clc
I0= 500; % maximum flow
Tc=60/72; % heart period
Ts=(2/5*Tc); % time in systole
P_ss=80; % diastolic pressure
R= 1;
C=1;
R1=0.05;
L=0.005;
I=@(t)I0*sin((pi*t)/Ts).^2.*(t<=Ts); %input current flow
Idot = @(t)I0*2*sin(pi*t/Ts).*cos(pi*t/Ts)*pi/Ts.*(t<=Ts);
Idotdot = @(t) I0*2*(cos(pi*t/Ts).^2 - sin(pi*t/Ts).^2)*(pi/Ts)^2.*(t<=Ts);
fun = @(t,y)[y(2);(Idotdot(t)*(R*L*C*R1)+Idot(t)*(L*(R+R1))+I(t)*(R*R1) - (y(2)*(C*R*R1+L)+y(1)*R1))/(L*C*R)];
y0 = [80 ;0];
tspan = [0 60/72];
[T,Y] = ode45(fun,tspan,y0);
plot(T,Y(:,1),'g')

Torsten on 23 Nov 2022
clear all
clc
I0= 500; % maximum flow
Tc=60/72; % heart period
Ts=(2/5*Tc); % time in systole
P_ss=80; % diastolic pressure
R= 1;
C=1;
R1=0.05;
L=0.005;
I=@(t)I0*sin((pi*t)/Ts).^2.*(t<=Ts); %input current flow
Idot = @(t)I0*2*sin(pi*t/Ts).*cos(pi*t/Ts)*pi/Ts.*(t<=Ts);
Idotdot = @(t) I0*2*(cos(pi*t/Ts).^2 - sin(pi*t/Ts).^2)*(pi/Ts)^2.*(t<=Ts);
fun = @(t,y)[y(2);(Idotdot(t)*(R*L*C*R1)+Idot(t)*(L*(R+R1))+I(t)*(R*R1) - (y(2)*(C*R*R1+L)+y(1)*R1))/(L*C*R)];
y0 = [80 ;0];
tspan = [0 60/72];
[T,Y] = ode45(fun,tspan,y0);
plot(T,Y(:,1),'g') function_of_time = @(t)interp1(T,Y(:,1),t);
function_of_time(30/72)
ans = 119.2901

Steven Lord on 24 Nov 2022
Call ode45 with one output argument. Pass that output from ode45 and an array of times into the deval function to evaluate the solution at those times.