RK 4th order for second order ODE
3 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
Hi, please is there a MATLAB code for RK 4th method 2nd order ODE. I have seen RK 4th for 1st order ODE. what I I need is a code for RK 4th order 2nd ODE (with a function handle). Which I can adjust based on my parameters. Thanks
2 commentaires
Jan
le 17 Nov 2018
It is very easy to convert a 2nd order ODE into a system of 1st order ODEs. Do you have a reason to avoid this?
Réponses (1)
khalida
le 14 Juil 2023
clear,clc
% % % % % RK4 system of odes higher order
h = 0.1;
x_beg = 0;
x_end = 0.7;
y_initial= 0;
z_initial= 0;
F_xy=@(x,z)(z);
F_xz=@(x,y,z)(-((1+5*x)/2*x*(x+1))*z-y^3+5*x+11*x^2+(8/27)*x^9);
x=x_beg:h:x_end;
y=zeros(1,length(x));
y(1)=y_initial;
z=zeros(1,length(x));
z(1)=z_initial;
for i=1:(length(x)-1);
i=1:(length(x)-1);
k1 = F_xy(x(i),y(i),z(i));
L1 = F_xz(x(i),y(i),z(i));
k2 = F_xy((x(i)+h/2),(y(i)+0.5*h*k1),z(i)+0.5*h*L1);
L2 = F_xz((x(i)+h/2),(y(i)+0.5*h*k1),z(i)+0.5*h*L1);
k3 = F_xy((x(i)+h/2),(y(i)+0.5*h*k2),z(i)+0.5*h*k2);
L3 = F_xz(x(i)+h/2,(y(i)+0.5*h*k2),(z(i)+0.5*h*L2));
k4 = F_xy((x(i)+h),(y(i)+k3*h),z(i)+L3*h);
L4 = F_xz((x(i)+h),(y(i)+k3*h),(z(i)+L3*h));
y(i+1) = y(i) + (1/6)*(k1+2*k2+2*k3+k4)*h;
z(i+1) = z(i) + (1/6)*(L1+2*L2+2*L3+L4)*h;
end
% plot(y,z)
figure(1)
plot(x,z)
hold on
plot(x,y)
0 commentaires
Voir également
Catégories
En savoir plus sur Ordinary Differential Equations dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!