I keep getting undefined function or variable h. This is my code to determine Euler's approximation for N=500 and N=5000
f=inline('2*y','t','y')
y(2)=y(1)+h*f(t(1),y(1)), t(2)=t(1)+h,
y(3)=y(2)+h*f(t(2),y(2)), t(3)=t(2)+h,
y(1)=3; t(1)=0; h = 0.1;
for n = 1:5
y(n+1)= y(n)+h*f(t(n),y(n));
t(n+1) = t(n)+h;
end
[t500,y500] = euler(f,[0,.5],3,500);
[t5000,y5000] = euler(f,[0,.5],3,5000);
t = linspace(0,.5,100); y = 3*exp(2*t); % evaluate the exact solution
plot(t500,y500,'ro-',t5000,y5000,'bx-',t,y,'k-'); axis tight;
legend('Euler N = 500','Euler N = 5000','Exact',2);
This is my function file:
function [t,y] = euler(f,tspan,y0,N)
% Solves the IVP y' = f(t,y), y(t0) = y0 in the time interval tspan = [t0,tf]
% using Euler's method with N time steps.
% Input:% f = name of inline function or function M-file that evaluates the ODE
% (if not an inline function, use: euler(@f,tspan,y0,N))
% For a system, the f must be given as column vector.
% tspan = [t0, tf] where t0 = initial time value and tf = final time value
% y0 = initial value of the dependent variable. If solving a system,
% initial conditions must be given as a vector.
% N = number of steps used.
% Output:
% t = vector of time values where the solution was computed
% y = vector of computed solution values.
m = length(y0);
t0 = tspan(1);
tf = tspan(2);
h = (tf-t0)/N; % evaluate the time step size
t = linspace(t0,tf,N+1); % create the vector of t values
y = zeros(m,N+1); % allocate memory for the output y
y(:,1) = y0'; % set initial condition
for n=1:N
y(:,n+1) = y(:,n) + h*f(t(n),y(:,n)); % implement Euler's method
end
t = t'; y = y'; % change t and y from row to column vectors
end
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