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codisinmyvines

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Feb 16th, 2022
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  1. function [y,x,iter]=VoltII_SimpleIter_Simpson(a,b,n,K,f,tol,y0)
  2. x=linspace(a,b,n);
  3. h=x(2)-x(1);
  4. rev_h=(n-1)/(b-a);
  5. F=f(x);
  6. if(nargin<=6) y0=F;
  7. end
  8. if(nargin<=5) tol=1e-10;
  9. end
  10. y=ones(1,n)*inf;
  11. yk=y0;
  12. iter=0;
  13. yk(1)=F(1);
  14. yk(2)=(F(2)+(h/2)*K(x(2),x(1))*yk(1))/...
  15. (1-(h/2)*K(x(2),x(2)));
  16. y(1)=F(1);
  17. y(2)=(F(2)+(h/2)*K(x(2),x(1))*y(1))/...
  18. (1-(h/2)*K(x(2),x(2)));
  19. A=[1,2*(1+mod(1:(n-3),2))]./3;
  20. while(norm(yk-y,inf)/norm(yk,inf)>tol)
  21. y=yk;
  22. iter=iter+1;
  23. for i=3:n
  24. j=1:i-2;
  25. yk(i)=(F(i)/h+sum(A(j).*K(x(i),x(j)).*y(j))+...
  26. (mod(i,2)*(1/2)+(5/6))*K(x(i),x(i-1))*y(i-1))/...
  27. (rev_h-1/(2+mod(i,2))*K(x(i),x(i)));
  28. end
  29. end
  30. end
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