Modifing Euler
This code works for four different methods for estimating IVPs. clear; a = 1; b = 2; alpha = -1/log(2); N = 10; h = (b - a)/N; t = a; w1 = alpha; %modified Euler w2 = alpha; %Heun w3 = alpha; %Midpoint w4 = alpha; %Runge-Kutta for i = 1:N tplusone = a + i * h; w1 = w1 + h/2 * (w1^2/(1+t) + (w1 + h*w1^2/(1+t))^2/(1+tplusone)); w2 = w2 + h/4 * (w2^2/(1+t) + 3*(w2 + (2/3) * h * w2^2/(1+t))^2/(1+(t+(2/3)*h))); w3 = w3 + h * (w3 + h/2 * w3^2/(1+t))^2/(1+(t + h/2)); k1 = h * w4^2/(1+t); k2 = h * (w4 + k1/2)^2/(1+(t+ h/2)); k3 = h * (w4 + k2/2)^2/(1+(t + h/2)); k4 = h * (w4 + k3)^2/(1+tplusone); w4 = w4 + 1/6 * (k1 + 2*k2 + 2*k3 + k4); t = tplusone; output(i,1) = i; output(i,2) = t; output(i,3) = w1; output(i,4) = w2; output(i,5) = w3; output(i,6) = w4; end output x=1.1:.1:2; y1 = -log(x+1).^-1 plot(x,y1,x,output(1:end , 3),x,output(1:end , 4),x,output(1:end , 5),x,output(1:end , 6))