Codes for R K 4th order simultaneous methods for n ODE

I want to solve n ODE by using RK 4 simultaneous method. please help me with proper code with example. atleast 4 equations.

[Kanishk Singhal]

Have you tried anything yet?

[Sam Chak]

@ARKA

Can you show the list of search results from Google?

I will pick and recommend from the list.

[John D'Errico]

Use ODE45. There are examples in the documentation of its use, as well as many other solvers.

If you insist on an explicit Runge-Kutta solve, then you will either need to write it yourself, OR you will need to find it on the File Exchange, where I am sure many students have effectively posted their homework.

[ARKA]

yea I am writing by my self, and thsts why I want to see some examples. with more number of equations.

[Torsten]

tstart = 0.0;
tend = 1.0;
h = 0.01;
T = (tstart:h:tend).';
Y0 = [1 -1];  
Y = runge_kutta_RK4(@f,T,Y0);
plot(T,Y) 
grid on

function Y = runge_kutta_RK4(f,T,Y0)
  N = numel(T);
  n = numel(Y0);
  Y = zeros(N,n);
  Y(1,:) = Y0;
  for i = 2:N
    t = T(i-1);
    y = Y(i-1,:);
    h  = T(i) - T(i-1);
    k0 = f(t,y);
    k1 = f(t+0.5*h,y+k0*0.5*h);
    k2 = f(t+0.5*h,y+k1*0.5*h);
    k3 = f(t+h,y+k2*h);
    Y(i,:) = y + h/6*(k0+2*k1+2*k2+k3);
  end
end 

function dy = f(t,y)
  B = 4;
  dy = [y(2) -exp(-B*t)-y(1)+5*exp(-2*t)-2*exp(-(B+2)*t)+exp(-B*t)+t];
end

Answer 1

[Mudit Kumar Bhugari]

Hi @ARKA

I understand that you want some examples for solving RK 4th Order Simulations. I'm sharing some resources with you which solves RK 4th Order Equations.

• https://in.mathworks.com/matlabcentral/answers/1703455-solving-for-two-variables-using-4th-order-runga-kutta-method
• https://in.mathworks.com/matlabcentral/answers/596755-4th-order-runge-kutta-code-that-can-solve-for-several-intial-conditions
• https://in.mathworks.com/matlabcentral/answers/465218-i-need-to-solve-these-4-equations-by-runge-kutta-4th-order-method-with-graphs

[ARKA]

got it