Successive over-relaxation (SOR)

Successive over-relaxation

June 2nd, 2008 by Daniel Høyer Iversen

Successive over-relaxation (SOR), written in Matlab to solve the Advection-diffusion equation. The matrix A (in A x= b) is a block pentadiagonal matrix.

 
function Z = solver(A,b)
%Successive over-relaxation, forbedret Gauss-Seidel
 
w=1.95;
 
p=params(0,0);
 
Z=p.noder(:,1)*0;
 
e=A(1,1);
 
for j=1:540
 
Z(1)= (1-w)*Z(1)+w/e*( b(1)- Z(2)*A(1,2)-Z(1+p.N)*A(1,1+p.N));
for i=2:p.N
Z(i)= (1-w)*Z(i)+w/e*( b(i)- Z(i-1)*A(i,i-1)-Z(i+1)*A(i,i+1)-Z(i+p.N)*A(i,i+p.N));
end
 
for i=p.N+1:p.NM-p.N
Z(i)= (1-w)*Z(i)+w/e*( b(i)- Z(i-p.N)*A(i,i-p.N)-Z(i-1)*A(i,i-1)-Z(i+1)*A(i,i+1)-Z(i+p.N)*A(i,i+p.N));
end
 
for i=p.NM-p.N+1:p.NM-1
Z(i)= (1-w)*Z(i)+w/e*( b(i)- Z(i-p.N)*A(i,i-p.N)- Z(i-1)*A(i,i-1)-Z(i+1)*A(i,i+1));
end
Z(p.NM)= (1-w)*Z(p.NM)+w/e*( b(p.NM)- Z(i-p.N)*A(i,i-p.N)-Z(p.NM-1)*A(p.NM,p.NM-1));
 
end

Do you want to use this code?

13 Responses to “Successive over-relaxation”

Daniel Høyer Iversen

http://en.wikipedia.org/wiki/Successive_over-relaxation :
Successive over-relaxation (SOR) is a numerical method used to speed up convergence of the Gauss–Seidel method for solving a linear system of equations. A similar method can be used for any slowly converging iterative process. It was devised simultaneously by David M. Young and by H. Frankel in 1950 for the purpose of automatically solving linear systems on digital computers. Over-relaxation methods have been used before the work of Young and Frankel. For instance, the method of Lewis Fry Richardson, and the methods developed by R. V. Southwell. However, these methods were designed for computation by human calculators, and they required some expertise to ensure convergence to the solution which made them inapplicable for programming on digital computers. These aspects are discussed in the thesis of David M. Young.

Jun 7th, 2008 3:29 pm
feby

tolong kirimkan program SOR dengan menggunakan matlab. thanks.

May 25th, 2009 6:21 am
hadi

hi
I am going to use this code but i am not sure it could help me to sove my problem or not. any way thanks a lot for your code.
best regards
hadi

Feb 14th, 2011 3:00 pm
majid

pls send me the code tq

hi
I am going to use this code but i am not sure it could help me to sove my problem or not. any way thanks a lot for your code.
best regards
hadi

Oct 16th, 2011 10:57 am
pauline

hi,

im going to use this code. plz send to me.
Thank you.

Best regard,
pauline

Oct 17th, 2011 10:51 am
garima

sor is a very useful method for calculating steady state probabilities. and this code indeed helps us to do that. thanks!

Oct 17th, 2011 12:07 pm
ned

I wiil try this code.
thanks.

Nov 18th, 2011 11:45 pm
Taylor Thompson

I plan to use this code in a demonstration on a project explaining SOR. Thanks for the hard work!

Dec 6th, 2011 11:28 pm
Sofoane

Thank you

Jun 16th, 2012 10:53 am
Daniel

Thanks!!!

Feb 12th, 2013 2:23 am
elea

hi
i wish this code help me to solve my probleeeeeeeeeeeeeeem

thanks

Mar 21st, 2013 9:41 pm
elea

thanks

Mar 21st, 2013 9:43 pm
twitter followers

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May 18th, 2013 3:26 pm

Programming

Successive over-relaxation

13 Responses to “Successive over-relaxation”

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