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ESTE PROGRAMA ES DESARROLLADO CON MATLAB
function RungeKuttaOS(f,h,y0,t0,tf)
% colocar en la ventana de matlab: RungeKutta4('f',h,y0,t0,tf)
% Metodo Runge-Kutta de orden superior para resolver una ecuacion
% diferencial ordinaria de la forma:
%
% dy
% -- = f(x,y) con condicion incial y(t0) = y0
% dx
disp('-------------------------------------------------------------------')
disp(' RUNGE-KUTTA DE ORDEN SUPERIOR ')
disp('-------------------------------------------------------------------')
x = t0;
y = y0;
Y = y';
X = x;
while x<tf
k1 = feval(f,x,y);
k2 = feval(f,x+(1/4)*h,y+(1/4)*k1*h);
k3 = feval(f,x+(1/4)*h,y+(1/8)*k1*h+(1/8)*k2*h);
k4 = feval(f,x+0.5*h,y-(1/2)*k2*h+k3*h);
k5 = feval(f,x+(3/4)*h,y+(3/16)*k1*h+(9/16)*k4*h);
k6 = feval(f,x+h,y-(3/7)*k1*h+(2/7)*k2*h+(12/7)*k3*h-(12/7)*k4*h+(8/7)*k5*h);
y = y + (7*k1+32*k3+12*k4+32*k5+7*k6)*h/90;
x = x + h;
Y = [Y;y'];
X = [X;x];
end
disp(' X Y');
[X Y]
grid on
plot(X,Y,'g')
title('Runge-Kutta de orden superior','color','B') <>
function RungeKuttaOS(f,h,y0,t0,tf)
% colocar en la ventana de matlab: RungeKutta4('f',h,y0,t0,tf)
% Metodo Runge-Kutta de orden superior para resolver una ecuacion
% diferencial ordinaria de la forma:
%
% dy
% -- = f(x,y) con condicion incial y(t0) = y0
% dx
disp('-------------------------------------------------------------------')
disp(' RUNGE-KUTTA DE ORDEN SUPERIOR ')
disp('-------------------------------------------------------------------')
x = t0;
y = y0;
Y = y';
X = x;
while x<tf
k1 = feval(f,x,y);
k2 = feval(f,x+(1/4)*h,y+(1/4)*k1*h);
k3 = feval(f,x+(1/4)*h,y+(1/8)*k1*h+(1/8)*k2*h);
k4 = feval(f,x+0.5*h,y-(1/2)*k2*h+k3*h);
k5 = feval(f,x+(3/4)*h,y+(3/16)*k1*h+(9/16)*k4*h);
k6 = feval(f,x+h,y-(3/7)*k1*h+(2/7)*k2*h+(12/7)*k3*h-(12/7)*k4*h+(8/7)*k5*h);
y = y + (7*k1+32*k3+12*k4+32*k5+7*k6)*h/90;
x = x + h;
Y = [Y;y'];
X = [X;x];
end
disp(' X Y');
[X Y]
grid on
plot(X,Y,'g')
title('Runge-Kutta de orden superior','color','B') <>
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