Runge-Kutta(Order 4) Algorithm using MATLAB (m-file)

MATLAB Programs:

% Runge-Kutta(Order 4) Algorithm

 % Approximate the solution to the initial-value problem

 % dy/dt=y-t^2+1 ; 0<=t<=2 ; y(0)=0.5;

 f = @(t,y) (y-t^2+1);

 a = input('Enter left end ponit, a:  ');

 b = input('Enter right end point, b:  ');

 n = input('Enter no. of subintervals, n: ');          % n=(b-a)/h

 alpha = input('Enter the initial condition, alpha:  ');

 h = (b-a)/n;

 t = a;

 w = alpha;

 fprintf('  t         w\n');

 fprintf('%5.3f %11.7f\n', t, w);

 for i = 1:n

   k1 = h*f(t,w);

   k2 = h*f(t+h/2.0, w+k1/2.0);

   k3 = h*f(t+h/2.0, w+k2/2.0);

   k4 = h*f(t+h,w+k3);

   w = w+(k1+2.0*(k2+k3)+k4)/6.0;

   t = a+i*h;

   fprintf('%5.3f %11.7f\n', t, w);

   plot(t,w,'b*'); grid on;

   xlabel('t values'); ylabel('w values');

   hold on;

 end

OUTPUTS:

Untitled3_rk4

Enter left end ponit, a:  0

Enter right end point, b:  2

Enter no. of subintervals, n: 10

Enter the initial condition, alpha:  0.5

  t         w

0.000   0.5000000

0.200   0.8292933

0.400   1.2140762

0.600   1.6489220

0.800   2.1272027

1.000   2.6408227

1.200   3.1798942

1.400   3.7323401

1.600   4.2834095

1.800   4.8150857

2.000   5.3053630

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