Array indices must be positive integers or logical values. Midpoint Method help

clc
clear all
close all

tic
h = 0.25 ; % Step size = 0.25
t = 0:h:2; % the range of x from 0 to 2 with a step size 0.25
y = zeros(1,length(t)); % matrix for allocate the y values
y_a = 2.02974 * 10^65; % analytical value at x=2
y(0) = 0 ; % initial value
n = numel(y);
func = @(x,y) (-200000 .* y + 200000 .* exp(-x) - exp(-x)); % the derivative function

for i=1:n-1 
    k_1 = func(t(i),y(i)); % to call the derivative function for k1
    k_2 = func(t(i)+0.5.*h,y(i)+0.5.*h.*k_1); % to call the derivative function for k2
    y(i+1) = y(i) + (h.*k_2);
end

E = (abs(y_a-y)/y_a)*100; %Relative error at x=2
toc

I try to solve the func equation with initial condition y(0)=0 but MATLAB gives me error which is

Array indices must be positive integers or logical values.

Error in Midpoint (line 10)
y(0) = 0 ; % initial value

Can you help asap?

Answer 1

[Jonas]

matlab's indexing starts with 1 and not with 0, the first element of y is y(1). maybe you wanted to write y(t==0)=0, which is the same as y(1)=0 here

[Muzaffer Cagislar]

so you mean that y(1) will be equal to actually x=0 right?

[Torsten]

@Muzaffer Cagislar

Your analytical solution is totally wrong.

y_a(x) = exp(-x)-exp(-200000*x)

which gives

y_a(2) = exp(-2)-exp(-400000)