# Runga Kutta method 4

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Ali on 20 Aug 2020
Commented: Ali on 13 Nov 2020
I want to solve this equation by Runga kutta method 4.
d2xd/dt2+0.2dx/dt-2.45xd+0.2908xp=
with intial condition
t=to=0
xd=1
xp=0
from t=0 to 100
Ali on 13 Nov 2020
I want to solve second order equation through Ruga kutta method .Please check what is error in this code
m=100;
k=25000;
e=100;
F=15000;
w=(k/m)^0.5;
t(1)=0;
x(1)=0;
v(1)=1;
h=0.1;
tfinal=100;
N=ceil((tfinal-t(1))/h);
f1=@(t,x,v) v;
f2=@(t,x,v) -(k/m)*v-(e/m)*x+(F/m)*cos(w*t);
for j=1:N;
t(j+1)=t(j)+h;
K1x=f1(t(j),x(j),v(j));
K1v=f2(t(j),x(j),v(j));
K2x=f1(t(j)+h/2,x(j)+h/2*K1x,v(j)+h/2*K1v);
K2v=f2(t(j)+h/2,x(j)+h/2*K1x,v(j)+h/2*K1v);
K3x=f1(t(j)+h/2,x(j)+h/2*K2x,v(j)+h/2*K2v);
K3v=f2(t(j)+h/2,x(j)+h/2*K2x,v(j)+h/2*K2v);
K4x=f1(t(j)+h,x(j)+h*K3x,v(j)+h*K3v);
K4v=f2(t(j)+h,x(j)+h*K3x,v(j)+h*K3v);
x(j+1)=x(j)+h/6*(K1x+2*K2x+2*K3x+K4x);
v(j+1)=v(j)+h/6*(K1v+2*K2v+2*K3v+K4v);
end
disp(x(N));
figure;
plot(t,x,'lineWidth',1);
xlabel('t');
ylabel('X','V');
hold on
vel(v(N));
figure;
plot(t,v,lineWidth',1);

Alan Stevens on 20 Aug 2020
Firstly, you can't have spaces in the name of the m-file. Remove them.
Secondly, remember "length" not "lenght".
Thirdly, pass parameters to the functions in the same order in which you define the functions.
Fourthly, make use of Matlab's error messages!
Here is a working code, but it produces nonsense because of the third point above. Put the parameters in the right order and you might get something sensible.
%input paramters
h=1;
t=1:h:100;
xd=zeros(1,length(t)); %%%%% length not lenght
xp=zeros(1,length(t)); %%%%% length not lenght
vd=zeros(1,length(t)); %%%%% length not lenght
vp=zeros(1,length(t)); %%%%% length not lenght
xdo=1;
vdo=0;
xpo=-1;
vpo=0;
xd(1)=xdo; %%%%% These next four lines must come after the previous four,
vd(1)=vdo; %%%%% and array indices start at 1 not 0 in Matlab.
xp(1)=xpo;
vp(1)=vpo;
%RK4
f1=@(t,xd,xp,vd,vp) vd;
f2=@(t,xd,xp,vd,vp) -0.4198*vd-5.9282*xd-1.5285*xp;
f3=@(t,xd,xp,vd,vp) vp;
f4=@(t,xd,xp,vd,vp) -0.4047*vp+1.5285*xp-7.3774*xd; %%%% xd not xp ?
for i=1:(length(t)-1) %%%%% length not lenght
%%%% The following parameters are not passed to the functions f1, f2,
%%%% etc in the order in which they are defined. You need to correct
%%%% that.
K1xd=f1(t(i),xd(i),vd(i), xp(i),vp(i));
K1vd=f2(t(i),xd(i),vd(i),xp(i),vp(i));
K1xp=f1(t(i),xp(i),vp(i), xd(i),vd(i));
K1vp=f2(t(i),xp(i),vp(i),xd(i),vd(i));
K2xd=f1(t(i)+h/2,xd(i)+h*K1xd/2,vd(i)+h*K1vd/2,xp(i)+h*K1xp/2,vp(i)+h*K1vp/2);
K2vd=f2(t(i)+h/2,xd(i)+h*K1xd/2,vd(i)+h*K1vd/2,xp(i)+h*K1xp/2,vp(i)+h*K1vp/2); %%%%%%%%%
K2xp=f1(t(i)+h/2,xp(i)+h*K1xp/2,vp(i)+h*K1vp/2,xd(i)+h*K1xd/2,vd(i)+h*K1vd/2);
K2vp=f2(t(i)+h/2,xp(i)+h*K1xp/2,vp(i)+h*K1vp/2,xd(i)+h*K1xp/2,vd(i)+h*K1vd/2); %%%%%%%%%
K3xd=f1(t(i)+h/2,xd(i)+h*K2xd/2,vd(i)+h*K2vd/2,xp(i)+h*K2xp/2,vp(i)+h*K2vp/2);
K3vd=f2(t(i)+h/2,xd(i)+h*K2xd/2,vd(i)+h*K2vd/2,xp(i)+h*K2xp/2,vp(i)+h*K2vp/2);
K3xp=f1(t(i)+h/2,xp(i)+h*K2xp/2,vp(i)+h*K2vp/2,xd(i)+h*K2xd/2,vd(i)+h*K2vd/2);
K3vp=f2(t(i)+h/2,xp(i)+h*K2xp/2,vp(i)+h*K2vp/2,xd(i)+h*K2xd/2,vd(i)+h*K2vd/2);
K4xd=f1(t(i)+h,xd(i)+h*K3xd,vd(i)+h*K3vd,xp(i)+h*K3xp,vp(i)+h*K3vp);
K4vd=f2(t(i)+h,xd(i)+h*K3xd,vd(i)+h*K3vd,xp(i)+h*K3xp,vp(i)+h*K3vp);
K4xp=f1(t(i)+h,xp(i)+h*K3xp,vp(i)+h*K3vp,xd(i)+h*K3xd,vd(i)+h*K3vd);
K4vp=f2(t(i)+h,xp(i)+h*K3xp,vp(i)+h*K3vp,xd(i)+h*K3xd,vd(i)+h*K3vd); %%%%%%% K4vp not K4vd
xd(i+1)=xd(i)+h/6*(K1xd+K1xp+2*K2xd+2*K2xp+2*K3xd+2*K3xp+K4xd+K4xp);
vd(i+1)=vd(i)+h/6*(K1vd+K1vp+2*K2vd+2*K2vp+2*K3vd+2*K3vp+K4vd+K4vp);
xp(i+1)=xp(i)+h/6*(K1xp+K1xd+2*K2xp+2*K2xd+2*K3xp+2*K3xd+K4xp+K4xd);
vp(i+1)=vp(i)+h/6*(K1vp+K1vd+2*K2vp+2*K2vd+2*K3vp+2*K3vd+K4vp+K4vd);
end
%plots
plot(t,xd)
hold on
plot(t,xp)
Ali on 13 Nov 2020
Thanks Alan