RK 4th order for second order ODE

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

[Jan]

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?

[Abraham]

Figured it out. Thanks, Jan.

Answer 1

[khalida]

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)