Runge-Kutta 3

how to use Runge Kutta 3 to solve an equation (2x''-x'²+4=0) for example.I have the initial values and the step sizes. Thanks

[Jan]

What have you tried so far? What exactly is "Runge Kutta 3"? Did you convert the equation of order 2 to a system of equations of order 1 already?

[James Tursa]

Are you supposed to write your own RK code or can you use a MATLAB solver such as ode45? (Nobody uses an RK3 method because in the derivation the error terms fall out naturally to produce an RK4 method).

[Abdelkarim Zribi]

intmin=0; intmax=1; numnodes=21; inival1=1; inival2=1; f1=@(t,x1,x2) 2*x2; f2=@(t,x1,x2) x1^2+4; h=(intmax-intmin)/(numnodes-1); t=zeros(1,numnodes); x1=zeros(1,numnodes); x2=zeros(1,numnodes); t(1)=intmin; x1(1)=inival1; x2(1)=inival2; for i=2:numnodes t(i)=t(i-1)+h; k11=f1(t(i-1),x1(i-1),x2(i-1)); k12=f1(t(i-1)+h/2,x1(i-1)+(h/2)*k11,x2(i-1)+(h/2)*k11); x1(i)=x1(i-1)+h*k12; x2(i)=x2(i-1)+h*f2(t(i-1),x1(i-1),x2(i-1)); end figure plot(t,x2,'.-')

this is what i wrote not sure if it's correct

[James Tursa]

Please format your code so that it is readable.

[Abdelkarim Zribi]

    intmin=0; 
    intmax=1; 
    numnodes=21; 
    inival1=1; 
    inival2=1; 
    f1=@(t,x1,x2) 2*x2; 
    f2=@(t,x1,x2) x1^2+4; 
    h=(intmax-intmin)/(numnodes-1);
    t=zeros(1,numnodes);
    x1=zeros(1,numnodes);
    x2=zeros(1,numnodes);
    t(1)=intmin;
    x1(1)=inival1;
    x2(1)=inival2; 
    for i=2:numnodes 
      t(i)=t(i-1)+h; 
      k11=f1(t(i-1),x1(i-1),x2(i-1));
      k12=f1(t(i-1)+h/2,x1(i-1)+(h/2)*k11,x2(i-1)+(h/2)*k11);
      x1(i)=x1(i-1)+h*k12;
      x2(i)=x2(i-1)+h*f2(t(i-1),x1(i-1),x2(i-1)); 
    end 
    figure 
    plot(t,x2,'.-')

[John D'Errico]

Please read this:

https://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup#answer_18099