MATLAB: I don not get the graph when i add A1(x) in the function f1=@(x,y) A1(x)+(1.3​3*pi*eta*y​^3)/(1+1.3​3*pi*eta*y​^3);

done

%clc
%clear all
eta=0.25;
L=2.5;
a=0.1;
h=0.1;
b=6;
x=a:h:b;
%%%%%%%%%%%%%%%%%%
A =@(x) (0<x).*1+(0<=x & x<=L).*(1+0.5*(1-cos(2*pi*x/L)).^1/2) + (L<x).*1;
A1=@(x) (gradient(A(x))./gradient(x));
f1=@(x,y) A1(x)+(1.33*pi*eta*y^3)/(1+1.33*pi*eta*y^3);
y(1)=01;
for i=1:length(x)-1;   
   k1=h*f1(x(i),y(i));
   k2=h*f1(x(i)+0.5*h,y(i)+.5*k1);
   k3=h*f1(x(i)+.5*h,y(i)+.5*k2);
   k4=h*f1(x(i)+h,y(i)+k3);
  y(i+1)=y(i)+(1/6)*(k1+2*k2+2*k3+k4);  
end
plot(x,y)

Best Answer

Do not use the for loop here. Let vectorisation work for you.
Try this: 
eta=0.25;
L=2.5;
a=0.1;
h=0.1;
b=6;
x=a:h:b;
%%%%%%%%%%%%%%%%%%
A =@(x) (0<x).*1+(0<=x & x<=L).*(1+0.5*(1-cos(2*pi*x/L)).^1/2) + (L<x).*1;
A1=@(x) (gradient(A(x))./gradient(x));
f1=@(x,y) A1(x)+(1.33*pi*eta*y.^3)./(1+1.33*pi*eta*y.^3);
y(1)=01;
% for i=1:length(x)-1;   
   k1=h*f1(x,y);
   k2=h*f1(x+0.5*h,y+.5*k1);
   k3=h*f1(x+.5*h,y+.5*k2);
   k4=h*f1(x+h,y+k3);
  y = +(1/6)*(k1+2*k2+2*k3+k4);  
% end
plot(x,y)
.
Related Question