How to make a UDF that calculates the Midpoint Rule

function output = Midpoint(f,a,b,h)

%%%%%%%% Inputs

% f - This is a function handle defining the right-hand side of the ODE we

% are solving, it should be a function of two arguments

% a - This is the initial x value

% b - This is the final x value where you want to approximate the solution

% to the ODE

% h - This is the step-size to use in determining the t-grid

%%%%%%%% Outputs

% t - This will be a vector of the t-grid values

% y - This will be a vector of the approximate solution evaluated at

% each of the t-grid values

deltax=(b-a)/h; %subintervals

x=[a:deltax:b]; %need to create a vector of n+1 evenly spaced points

mpr=0; %initialize midpoint rule

for k=1:h;

mpr=mpr+f((2*k+1)/2)*deltax;

output=mpr

end

end

this is what i HAVE SO FAR

Answer 1

[Alan Stevens]

Don't confuse x with t! The following might help. I'll leave you to turn it into a function:

f = @(x,y) x+y; % function of two arguments  f = dy/dx  (y = 2exp(x)-x-1)
a = 0;          % lower limit
b = 1;          % upper limit
n = 100;        % number of intervals
deltax=(b-a)/n; % stepsize
x = a:deltax:b; % vector of evenly spaced points 
y = zeros(size(x)); % storage space for y.
y(1) = 1;       % initial value for y

for i = 1:n
    mpx = x(i) + deltax/2;       % midoint between x(i) and x(i+1)
    mpy = y(i) + y(i)*deltax/2;  % value of y at midpoint
   y(i+1)= y(i)+f(mpx,mpy)*deltax;  % explicit midpoint rule 
end
plot(x,y),grid