ODE Midpoint Method Help

6 次查看（过去 30 天）

Camila Gill 2020-3-13

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/510633-ode-midpoint-method-help

评论： James Tursa 2020-3-13

Trying to write a function that implements 1-step of ODE Runge Kutta Midpoint Method. Function references another function containing eqaution (not sure if fn calls function correctly).

The function will not solve for k1 and k1 therfore i can not solve for y(i+1).

Please help.

% Implements 1-step of Mid-point Method
function xnew = midpointstep_CGill(tint, x, h, fn)
    global ode    
    syms x(t) dx(t)
    h = .01;                % Step Size
    tint = 0:h:25;          % Time interval [mint, maxt]
    x(0) == 0;              % Inital Condition  
    dx(0) == 30;            % Inital Condition             
    fn = ode3dp_CGill(ode);
    
    for i = 1:(length(tint)-1)
        k1 = fn(x(i),dx(i));
        k2 = fn(x(i) + 0.5*h, dx(i) + 0.5*h*k1);
        
        y(i+1) = y(i) + k2*h;
    end 
end

Calls the following function

% Computes ODE values
function ode = ode3dp_CGill(t,x)
    global ode
    syms x(t) dx(t) m b k F(t)
    F = -sin(4*pi*t);
    eq = m*dx(t) + b*x(t) + k*x == F;
    eq = subs(eq, [b], [2*(k*m)^(1/2)]);
    ode = collect(eq, m)/m;
end