MATLAB: Runge-Kutta method related

ode45runge-kutta method

   I have a doubt (rather a confusion) in Ruge-Kutta method. I want to time integrate an equation of the form
                 dy/dt = g*n-0.5*(u^2+v^2)

Where g,n,u and v are known. So I can put equation in the form

                  dy/dt = a constant

I want to time integrate it in the time span [ti tf]. As the equation have constant on right side and no time, no y variable, how I can time integrate it? I have initial conditions for y. If I use ode45 how I can call ode45? How the equation should be fed to ode45?

Thanks in advance

Sreenu

Best Answer

Why are you bothering to use ode45 at all?

Your solution for any t >= ti is just

y = y0 + (t - ti) * (g*n-0.5*(u^2+v^2));

Related Solutions

MATLAB: 4th order Runge-Kutta code that can solve for several intial conditions

Here's a version:

% Initial conditions
t0=0;
x0=0:0.2:1;
y0=1:0.2:2;
dt=0.1;
tz=1;
t_range= t0:dt:tz;
X = zeros(numel(x0),numel(t_range));
Y = zeros(numel(y0),numel(t_range));
x_rk=zeros(1,numel(t_range));
y_rk= zeros(1,numel(t_range));
for n = 1:numel(x0)
    x_rk(1)=x0(n);
    y_rk(1)=y0(n);
    for i=1:length(t_range)-1
        [x_rk(i+1), y_rk(i+1)]=rk_method(x_rk(i),y_rk(i),dt);
    end
    X(n,:) = x_rk;
    Y(n,:) = y_rk;
    %% PLots
    subplot(numel(x0)/2,2,n)
    plot (t_range, x_rk,'b-o',t_range, y_rk,'y-o','MarkerSize',5);
    grid
    title([num2str(x0(n)),'   ',num2str(y0(n))])
    legend('x','y')
end
disp('X = '), disp(X)
disp('Y = '), disp(Y)
%% Functions
function [dxdt, dydt]= f(x,y)
dxdt =  5*x-3*y;
dydt = -6*x+2*y;
end 
function [x1, y1]=rk_method(x0,y0,dt)
[k11, k12]=f(x0,y0);     
[k21, k22]=f(x0+0.5*dt*k11,y0+0.5*dt*k12); 
[k31, k32]=f(x0+0.5*dt*k21,y0+0.5*dt*k22); 
[k41, k42]=f(x0+dt*k31, y0+dt*k32); 
x1=x0+dt*((k11/6)+((k21+k31)/3)+(k41/6));
y1=y0+dt*((k12/6)+((k22+k32)/3)+(k42/6));
end

MATLAB: Use of ode45 for projectile trajectory including drag

To solve this system, create a function ode_func containing the equations:

function dy = ode_func(x,y)
k = 1;
g = 9.8;
v = sqrt(y(1)^2+y(2)^2);
dy = zeros(4,1);    
dy(1) = -k*v;
dy(2) = (-k*v*y(2)-g)/y(1);
dy(3) = 1/y(1);
dy(4) = y(2)/y(1);

And solve with ode45:

[X,Y] = ode45(@ode_func,...

Best Answer

Related Solutions

MATLAB: 4th order Runge-Kutta code that can solve for several intial conditions

MATLAB: Use of ode45 for projectile trajectory including drag

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