% Input: interval inter, initial value y0, number of steps n
% Output: time steps t, solution y
% Example usage: midpoint([0 1],1,10);
function [t,y]=midpoint(inter,y0,n)
t(1)=inter(1); y(1)=y0;
h=(inter(2)-inter(1))/n;
correct(1) = 1;
for i=1:n
t(i+1)=t(i)+h;
disp("t value: " + t(i+1));
y(i+1)=midpointstep(t(i),y(i),h);
disp("Midpoint approx: " + y(i+1));
error=abs(y(i+1)-(exp((1/3)*t(i+1)^3)));
disp("Error " + error);
disp(" ");
end
plot(t,y)
function y=midpointstep(t,y,h)
%one step of Euler’s Method
%Input: current time t, current value y, stepsize h
%Output: approximate solution value at time t+h
s1 = ydot(t,y);
s2 = ydot(t+h/2, y+h*s1/2);
y=y+h*s2;
function z=ydot(t,y)
%right-hand side of differential equation
z=t^2*y;