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How solve Thomas algorithm in two step?

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ghasem_008

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hi.
as you know,tridiagonal matrix algorithm (TDMA), known as the Thomas algorithm.and a
tridiagonal system may be written as :
a(i)*x(i-1) + b(i)*x(i) + c(i)*x(i+1) =d(i) ; a(1)=0; c(n)=0;

now,I have one question:
I must to decompose d(i) to two part.i,e:
suppose d(i) is : d(i) = e(i) + f(i).
I want to slove thomas algorithm in two section:
first:
with e(i) in right hand side only.i,e : 0.5*[ a(i)*x(i-1) + b(i)*x(i) + c(i)*x(i+1) ] = e(i)
second:
with f(i) in right hand side only.i,e : 0.5* [a(i)*x(i-1) + b(i)*x(i) + c(i)*x(i+1)] = f(i)

can I solve this algorithm in two step?i,e in this manner,
answers [x(i)] in second part end are same as x(i) in original problem?

thanks...
 

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