Never-Never-Land

How to use: ODEREN offers an web interface for users to define their ODEs, the solutions parameters, such as time span, time interval and solution methods etc. Then the program will automatically generate a matlab code that solves the user's specific problem. The results will be exported to output.txt with first columns - time, other columns - y.

PROBLEM DESCRIPTION

% problem description examples dy = [y(2); -y(1)-0.1*y(2)-sin(t)]; % or in the matrix form K = [0 1; -1 -0.1]; b = [0; -sin(t)]; dy = K*y + b; % for implicit method, dy is not necessary % for implicit methods, you must use the matrix form

INITIAL VALUES

% initial value examples y0 = [1; 0];

SOLUTION TIME

% solution time description time = 0:0.1:20; % time definition auto_time = false; % define the time interval autimatically or not

SOLUTION METHOD Explicit: Euler-forward Explicit: Improved Euler Explicit: Runge-Kutta 4 Implicit: Euler-backward - linear K Implicit: Euler-theta - linear K Implicit: Runge-Kutta 3 - linear K (for stiff problem)

% solution parameters theta = 0.5; % E.G. Euler-theta method

Aug.14, 2017 update notes: i added RK3 method, which is stable for stiff problems.

Aug.13, 2017 update notes: i added Euler-forward, improved Euler, RK4, Euler-backward and Euler-theta methods.