ajadnumerical1.m

% Numerical Experiment- program for all  Euler, Midpoint, Adams-Bashforth Runge - Kutta method 
clear all 
clc
fprintf(' enter the value of h =    ')  % for diff value of h
h=input(' ');                           % enter the value of h
hold on
x=0;
t=0:(0.5):3;        % time - step

  fprintf(' euler for n=1\n midpoint for n=2\n adams Bashforth for n=3\n RK-4 for n=4\n')
  fprintf(' enter the value of n =  ')  
  n=input(' ');                         % enter the choice of methods 
  % program for Eulers method
  if n==1
      for i=1:6
          k1=exp(cos(t(i)*x(i)))*h;
          x(i+1)=x(i)+k1
          
          format long
      end
x_at_3s= x(7)
          plot(t,x)
          xlabel('t')
          ylabel('x')
          axis 'square'
          
          
          % program for midpoint method
  elseif n==2
    for i=1:6          
          k1=exp(cos(t(i)*x(i)));
          k2=x(i)+exp(cos(t(i)*x(i)))*(h/2);
          k3=exp(cos((t(i)+(h/2))*k2));
          x(i+1)=x(i)+h*k3
          format long
      end
         x_at_3s= x(7)
          plot(t,x)
          xlabel('t')
          ylabel('x')
          axis 'square'
          
          
         % program for adams Bashforth method 
  elseif n==3
      for j=1:3
         k1=exp(cos(t(j)*x(j)));
         k2=exp(cos((t(j)+0.5*h)*(x(j)+0.5*h*k1)));
         k3=exp(cos((t(j)+0.5*h)*(x(j)+0.5*h*k2)));
         k4=exp(cos((t(j+1))*(x(j)+h*k3)));
         x(j+1)=x(j)+(1/6)*h*(k1+2*k2+2*k3+k4);
      end
     for j=4:6
         x(j+1)=x(j)+(h/24)*(55*exp(cos(t(j)*x(j)))-59*exp(cos(t(j-1)*x(j-1)))+37*exp(cos(t(j-2)*x(j-2)))-9*exp(cos(t(j-3)*x(j-3))))
  
   format long
     end
      x_at_3s= x(7)
          plot(t,x)
          xlabel('t')
          ylabel('x')
          axis 'square'
          
          
          % program for Runge-kutta method
          elseif n==4
for i=1:6
    k1=exp(cos(t(i)*x(i)));
    k2=exp(cos((t(i)+0.5*h)*(x(i)+0.5*h*k1)));
    k3=exp(cos((t(i)+0.5*h)*(x(i)+0.5*h*k2)));
    k4=exp(cos((t(i+1))*(x(i)+h*k3)));
    x(i+1)=x(i)+(1/6)*h*(k1+2*k2+2*k3+k4)
    format long
end
    x_at_3s= x(7)
    plot(t,x)
    xlabel('t')
    ylabel('x')
    axis 'square'
  end