Hi,
Computing a numerical integration with the Midpoint Method I’m struggling with the output of my function, while with Euler I got the expected result, with this method I’m getting a different graphical solution far away than the analytical solution (and the euler’s one). What could be wrongly specified?
Thanks for your help.
% Midpoint method
% General information
L = 0.61; % [m]
G = 9.81; % gamma [m/s^2]

% Sampling interval
h = 0.1;
%h = 0.05;
%h = 0.01;

ti = 0; % Initial time
tf = 4; % Final time
t = ti:h:tf; % Time vector

function [md] = midpoint(t,L,G,h)
% Initial Value problem
md = zeros(2, length(t));
md(1,1) = pi/40;

for i = 1:length(t)-1
pmd = md(2,i) + (h/2) + (-G/L)*sin(md(1,i)) + (h/2) * [md(2,i); (-G/L)*sin(md(1,i))];
md(:,i+1) = md(:,i) + h * pmd;
end
endHi,
Computing a numerical integration with the Midpoint Method I’m struggling with the output of my function, while with Euler I got the expected result, with this method I’m getting a different graphical solution far away than the analytical solution (and the euler’s one). What could be wrongly specified?
Thanks for your help.
% Midpoint method
% General information
L = 0.61; % [m]
G = 9.81; % gamma [m/s^2]

% Sampling interval
h = 0.1;
%h = 0.05;
%h = 0.01;

ti = 0; % Initial time
tf = 4; % Final time
t = ti:h:tf; % Time vector

function [md] = midpoint(t,L,G,h)
% Initial Value problem
md = zeros(2, length(t));
md(1,1) = pi/40;

for i = 1:length(t)-1
pmd = md(2,i) + (h/2) + (-G/L)*sin(md(1,i)) + (h/2) * [md(2,i); (-G/L)*sin(md(1,i))];
md(:,i+1) = md(:,i) + h * pmd;
end
end Hi,
Computing a numerical integration with the Midpoint Method I’m struggling with the output of my function, while with Euler I got the expected result, with this method I’m getting a different graphical solution far away than the analytical solution (and the euler’s one). What could be wrongly specified?
Thanks for your help.
% Midpoint method
% General information
L = 0.61; % [m]
G = 9.81; % gamma [m/s^2]

% Sampling interval
h = 0.1;
%h = 0.05;
%h = 0.01;

ti = 0; % Initial time
tf = 4; % Final time
t = ti:h:tf; % Time vector

function [md] = midpoint(t,L,G,h)
% Initial Value problem
md = zeros(2, length(t));
md(1,1) = pi/40;

for i = 1:length(t)-1
pmd = md(2,i) + (h/2) + (-G/L)*sin(md(1,i)) + (h/2) * [md(2,i); (-G/L)*sin(md(1,i))];
md(:,i+1) = md(:,i) + h * pmd;
end
end midpoint, numerical integration, for loop, function, indexing, iteration MATLAB Answers — New Questions

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