Runge-Kutta_4th_Order_method

Runge-Kutta 4th Order method

clc;
clear all;
close all;
h=0.01;
a=0;
b=1.8; 
x = a:h:b;           
y = zeros(1,numel(x));
y(1)= 1;
Fyx = @(x,y) (y^2-x^2)/(y^2+x^2);
fprintf('%7s %7s %7s %7s %7s %7s %7s \n','i','x(i)','k1','k2','k3', 'k4','y(i)');
for i=1:1:numel(x)      
    k1 = h*Fyx(x(i),y(i));
    k2 = h*Fyx(x(i)+0.5*h,y(i)+0.5*k1);
    k3 = h*Fyx((x(i)+0.5*h),(y(i)+0.5*k2));
    k4 = h*Fyx((x(i)+h),(y(i)+k3));
    y(i+1) = y(i) + (1/6)*(k1+2*k2+2*k3+k4); 
    if x(i)==0.2 || x(i)==1.8
    fprintf('%7d %7.2f %7.3f %7.3f',i, x(i), k1, k2);
    fprintf(' %7.3f %7.3f %7.3f \n', k3, k4, y(i+1));
    end
end

    y(numel(x))=[ ];
  
    plot(x,y)
    title('RK-4');
    ylabel('y');  
    xlabel('x');
    grid on