Chemical Engineering Hand Written_Notes_Part_34

Chemical Engineering Hand Written_Notes_Part_34 - 70 3....

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70 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES the above set of n equations can be rearranged as (3.65) A α 2 = b where A is a ( n +1) × ( n and Y is ( n vector. Elements of A and b can be obtained from equations (3.61-3.63). Note that matrix A will be a near tridiagonal matrix. 3.2. Algorithms for Solving Sparse Linear Systems [ 5 ] . 3.2.1. Thomas Algorithm for Tridiagonal and Block Tridiagonal Matrices. Consider system of equation given by following equation (3.66) b 1 c 1 0 ... ... ... ... 0 a 2 b 2 c 2 0 ... ... ... 0 0 a 3 b 3 c 3 ... ... ... 0 00 a 4 b 4 c 4 . ... ... ... ... ... .. ... ... ... ... ... ... ... ... ... ... ... c n 2 0 ... ... ... ... ... a n 1 b n 1 c n 1 0000 ... . 0 a n b n x 1 x 2 x 3 .... .... .... .... x n = d 1 d 2 .... .... .... .... .... d n where matrix A is a tridiagonal matrix.
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Chemical Engineering Hand Written_Notes_Part_34 - 70 3....

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