Runga Kutta method 4

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Ali
Ali il 20 Ago 2020
Commentato: Ali il 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
  3 Commenti
Ali
Ali il 20 Ago 2020
This is my code but it does not run.This code is for two equation of similar kind.But if one equation code run that s also ok.
Ali
Ali il 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);

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Risposta accettata

Alan Stevens
Alan Stevens il 20 Ago 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)
  6 Commenti
Alan Stevens
Alan Stevens il 13 Nov 2020
Try it. It works, it's just a boring result!
Ali
Ali il 13 Nov 2020
Thanks Alan

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