RangaKutta Method Vs Analytic Method plot problem

 x_a=linspace(0,2,n)
     h=x_a(n)-x_a(n-1)
     y_a=((x_a.^2+1/2.*x_a+1)).^2
     y_r(1)=1;
     for i=1:n-1 ;
     
     x_r=linspace(0,2,n)
     h_r=x_r(n)-x_r(n-1);
     k2_x(i)=x_r(i)+h_r/2;
     k1(i)=(1+4.*x_r(i)).*sqrt(y_r(i));
     k2_y(i)=y_r(i)+k1(i)./2;
     k2(i)=(1+4.*(k2_x(i)).*sqrt(k2_y(i)));
     k3_y(i)=y_r(i)+k2(i)./2;
     k3(i)=(1+4.*k2_x(i)).*sqrt(k3_y(i));
     k4_x(i)=x_r(i)+h_r;
     k4_y(i)=y_r(i)+k3(i);
     k4(i)=(1+4.*k4_x(i)).*sqrt(k4_y(i));
     y_r(i+1)=y_r(i)+h_r.*(k1./6+k4./6+k2./3+k3./3)
     i=i+1;
     plot(x_a,y_a,'--kd')
     hold on
     plot(x_r,y_r,'--y+')
     end

This is program to plot graph between RangaKutta Method Vs Analytic Method.

But the dont know why the graph is not plotting.Its giving the value of y_r ,two times only.Although it should give the values n times.

Answer 1

[Walter Roberson]

n = 128;
x_a=linspace(0,2,n)

x_a = 1×128

0 0.0157 0.0315 0.0472 0.0630 0.0787 0.0945 0.1102 0.1260 0.1417 0.1575 0.1732 0.1890 0.2047 0.2205 0.2362 0.2520 0.2677 0.2835 0.2992 0.3150 0.3307 0.3465 0.3622 0.3780 0.3937 0.4094 0.4252 0.4409 0.4567

     h=x_a(n)-x_a(n-1)

h = 0.0157

     y_a=((x_a.^2+1/2.*x_a+1)).^2

y_a = 1×128

1.0000 1.0163 1.0338 1.0524 1.0722 1.0932 1.1155 1.1391 1.1639 1.1902 1.2178 1.2468 1.2774 1.3094 1.3429 1.3781 1.4148 1.4533 1.4935 1.5355 1.5792 1.6249 1.6725 1.7221 1.7738 1.8275 1.8834 1.9415 2.0020 2.0647

     y_r(1)=1;
     for i=1:n-1 ;
     
     x_r=linspace(0,2,n)
     h_r=x_r(n)-x_r(n-1);
     k2_x(i)=x_r(i)+h_r/2;
     k1(i)=(1+4.*x_r(i)).*sqrt(y_r(i));
     k2_y(i)=y_r(i)+k1(i)./2;
     k2(i)=(1+4.*(k2_x(i)).*sqrt(k2_y(i)));
     k3_y(i)=y_r(i)+k2(i)./2;
     k3(i)=(1+4.*k2_x(i)).*sqrt(k3_y(i));
     k4_x(i)=x_r(i)+h_r;
     k4_y(i)=y_r(i)+k3(i);
     k4(i)=(1+4.*k4_x(i)).*sqrt(k4_y(i));
     y_r(i+1)=y_r(i)+h_r.*(k1./6+k4./6+k2./3+k3./3)
     i=i+1;
     plot(x_a,y_a,'--kd')
     hold on
     plot(x_r,y_r(1:end-1),'--y+')  %CHANGED
     end

x_r = 1×128

0 0.0157 0.0315 0.0472 0.0630 0.0787 0.0945 0.1102 0.1260 0.1417 0.1575 0.1732 0.1890 0.2047 0.2205 0.2362 0.2520 0.2677 0.2835 0.2992 0.3150 0.3307 0.3465 0.3622 0.3780 0.3937 0.4094 0.4252 0.4409 0.4567

y_r = 1×2

1.0000 1.0190

x_r = 1×128

0 0.0157 0.0315 0.0472 0.0630 0.0787 0.0945 0.1102 0.1260 0.1417 0.1575 0.1732 0.1890 0.2047 0.2205 0.2362 0.2520 0.2677 0.2835 0.2992 0.3150 0.3307 0.3465 0.3622 0.3780 0.3937 0.4094 0.4252 0.4409 0.4567

Unable to perform assignment because the left and right sides have a different number of elements.

Notice in

          y_r(i+1)=y_r(i)+h_r.*(k1./6+k4./6+k2./3+k3./3)

that the k* variables are vectors.