MATLAB: I keep getting this Attempted to access y(1.5); index must be a positive integer or logical. when trying to implement a numerical hybrid scheme involving y(i+1/2) . here’s the code so far: the problem is in line36

errorhybridscheme

function[x,y]=secondode1(x0,x1,y0,z0,n)
format long 
f=@(x,y,z)z;
g=@(x,y,z) -6/x*z-4/x^(2)*y;
x0=1;
x1=0.003125;
y0=1;
z0=1;
n=10;
h=0.003125;
%preallocation space for x and y
%yy and xx means yexact and xexact respectively
x=[x0,zeros(1,15)];
y=[y0,zeros(1,15)];
z=[z0,zeros(1,15)];
xx=zeros(1,15);
yy=zeros(1,15);
for i=1:3
    x(i+1)=x(i)+h;
    k1=h*f(x(i),y(i),z(i));
    l1=h*g(x(i),y(i),z(i));
    k2=h*f(x(i)+(h/2),y(i)+(k1/2),z(i)+(l1/2));
    l2=h*g(x(i)+(h/2),y(i)+(k1/2),z(i)+(l1/2));
    k3=h*f(x(i)+(h/2),y(i)+(k2/2),z(i)+(l2/2));
    l3=h*g(x(i)+(h/2),y(i)+(k2/2),z(i)+(l2/2));
    k4=h*f(x(i)+h,y(i)+k3,z(i)+l3);
    l4=h*g(x(i)+h,y(i)+k3,z(i)+l3);
    k=(k1+(2*k2)+(2*k3)+k4)/6;
    l=(l1+(2*l2)+(2*l3)+l4)/6;
    y(i+1)=y(i)+k;
    z(i+1)=z(i)+l;
end
for i=1:10
   x(i+1)=x(i)+h;
   y(i+2)=-3*y(i)+4*y(i+1/2)+(h^(2))/32*(f(x(i+2),y(i+2),z(i+2))+38*f(x(i+1),y(i+1),z(i+1))+9*f(x(i),y(i),z(i)));
    xx(i+1)=xx(i)+h;
    yy(i+1)=xx(i)+h;
    yy(i+1)=(5*x.^3-2)/(3*x.^4);
end
y,yy
plot(x,y,'g-')
hold on
plot(xx,yy,'r:')
xlabel('x axis'),ylabel('y axis'),title('the graph f the scheme solution and exact solution'),legend('scheme','exact')
for i=1:10
  [[y(i+2)]' [yy(i+1)]']
  error=[y(i+2)-yy(i+1)]
end
end

Best Answer

You can't call an index of an array with non-positive integer arguments. There is no 3/2 th entry of a matrix or vector, that doesn't make any sense.
Therefore y(i+1/2) will obvious return an error if i is an integer, do you perhaps mean to write y((i+1)/2) or (y(i)+y(i+1))/2?
David
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