Help needed with plotting errors of Euler's method vs h on loglog axes

Hi,

The question I am attempting is applying Euler's Method to solve y' = f(t, y), a <= t b <= y(a) = y0 with time-step h = 2^-(i+1), i = 1, 2, . . . , 16. For each value of h, computing the corresponding maximum of the absolute value of the error. I've also provided a table with two columns containing h and the corresponding maximum errors, and 'plotted' these errors versus h in a figure with double-log axes.

My issue is with the plotting of the errors versus h. Here is my code:

N2 = 16;

h = zeros(N2,1);

error = zeros(N2,1);

%a = 0;

%b = 4;

%T = 4;

y0 = -1;

for i = 1:N2

h(i) = 2^(-(i-1));

N2 = T/h(i);

[t,w] = Euler(0,T,N2,y0,f);

error(i) = abs(ysol(T)-w(end));

end

% creating table

format long

table(h,error,'VariableNames',{'h','error'})

% creating loglog plots

loglog(h,error,'r', 'linewidth',1.5)

hold on

loglog(h, h, 'm','linewidth',1.5)

xlabel('h')

legend('error','O(h)');

title('Plot of errors of Eulers method vs h','fontsize',15)

I've put in bold the part I'm having trouble with. When I plot the graph, i get two straight lines that are far away from each other, but I think i need the lines to closely follow one another. What am I doing wrong?

Thank you kindly for your help in advance!

Answer 1

[Harsha Priya Daggubati]

Hi,

Could you check on the reason why you intend to plot double-log axes with:

1. h and error
2. h and h

You mentioned you want to plot 'h' and its corresponding 'error' value, it is confusing why you need the above 2nd plot.