Question

In this exercise, your will be creating the function euler2 which applies Euler's method to numerically solve a first order ODE, but with no overshoot.

Input variables:

ODEFUN	–	A function representing the the equation for y'. It must be a function of t and y.
TSPAN	–	a vector containing the start time and end time (TSPAN = [tStart,tEnd]).
Y0	–	The value for y at tStart.
h	–	The step size.

Output variables:

TOUT	–	The output time vector.
YOUT	–	The output y vector.

Solution Process

The function should numerically solve the first order ODE y' = ODEFUN using Euler's method. Euler's method will need to be programmed with a while loop. The loop should compute the next values in TOUT and YOUT while the current value for TOUT is less than tEnd. If the simulation does overshoot, it should change the final value for h so that the simulation finishes exactly at tEnd. For example, with a start time of 0, end time of 1, and a step size of 0.3, TOUT will be [0,0.3,0.6,0.9,1].

Notes:

This is a continuation from the previous problem euler. We suggest that you simply modify your previous code to help solve this problem.

Potentially Useful Functions: while, if, end

Banned Functions: for

Function Template:

function [TOUT,YOUT] = euler2(ODEFUN,TSPAN,Y0,h)

%insert answer here

end

Answer 1

function [TOUT,YOUT] = euler2(ODEFUN,TSPAN,Y0,h)
t=TSPAN(1);
k=1;
TOUT(1)=t;
YOUT(1)=Y0;
tlim=TSPAN(2);
while t < tlim
k=k+1;
m=ODEFUN(t,Y0);
if (t+h)>TSPAN(2)
h=h-(t+h-TSPAN(2));
end
y=Y0+h*m;
  

t1=t+h;
TOUT(k)=t1;
YOUT(k)=y;
t=t1;
Y0=y;
end