Index exceeds number of array elements (1) Heuns method

% step size %
h = 0.1; 

% number of steps % 
N = 10;

x(1) = 0.1;
y(1) = 1.1;
f =  2*sin(x)+y;
for i = 1:N
    y(i+1) = y(i) + (h/2) * f(x(i),y(i)) + f(x(i+1),y(i+1)),
    y(i) + h * f(x(i),y(i));
    x(i+1) = x(i)+h;
end

plot(x,y)

Answer 1

[KALYAN ACHARJYA]

Please verify (Read): Heuns Method

h = 0.1; 
% number of steps % 
N = 10;
y=zeros(1,N);
x=zeros(1,N);
x(1) = 0.1;
y(1) = 1.1;
f =@(x,y) 2*sin(x)+y;
for i = 1:N
    c1=f(x(i),y(i));
    c2=f(x(i)+h,y(i)+c1*h);
    y(i+1)=y(i)+(h/2)*(c1+c2);
    x(i+1)=x(i)+h;
end
plot(x,y)

[Darren Tharby]

Thankyou

Answer 2

[VBBV]

% step size %
h = 0.1; 
% number of steps % 
N = 10;
x = zeros(1,N);
y = zeros(1,N);
yt = zeros(1,N);
x(1) = 0.1;
y(1) = 1.1;
f =  @(x,y) 2*sin(x)+y;
for i = 2:N
    yt(i) =  y(i-1) + h * f(x(i-1),y(i-1)); % intermediate approximation  
    y(i) = y(i-1) + (h/2) * (f(x(i-1),y(i-1)) + f(x(i-1),yt(i)));
    x(i) = x(i-1)+h;
end

plot(x,y,'linewidth',2);
hold on;
plot(x,yt,'ro','MarkerSize',6,'MarkerFaceColor','red')
legend('Final approx','Intermediate approx')

You have to modify the intermediate values step to get final approximation,