Chemical Engineering Hand Written_Notes_Part_37

Chemical Engineering Hand Written_Notes_Part_37 - 76 3....

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76 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES This condition is practically equivalent to the previous condition. Equation (4.16) is more suitable from the view point of programming than equation (4.3) and the algorithm can be stated as follows: Jacobi Algorithm INITIALIZE : b ,A, x (0) ,k max k =0 δ =100 ε WHILE [( δ>ε ) AND ( k<k max )] FOR i =1: n r i = b i n P j =1 a ij x (0) j x (1) i = x (0) i +( r i /a ii ) END FOR δ = k r k / k b k k = k +1 x (0) = x (1) END WHILE 4.2. Gauss-Seidel Method. When matrix A is large, there is a practical di culty with the Jacobi method. It required to store all components of x ( k ) in the computer memory (as a separate variables) until calculations of x ( k +1) is over. The Gauss-Seidel method overcomes this di cu ltybyus ing x ( k +1) i imme- diately in the next equation while computing x ( k +1) i +1 . This modi f cation leads to the following set of equations (4.21) x ( k +1) 1 =[ b 1 a 12 x ( k ) 2 a 13 x ( k ) 3 ...... a 1 n x ( k ) n ] /a 11 (4.22) x ( k +1) 2 b 2 n a 21 x ( k +1) 1 o n a 23 x ( k ) 3 + ..... + a 2 n x ( k ) n o ] /a 22 (4.23) x ( k +1) 3 b 3
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This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

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Chemical Engineering Hand Written_Notes_Part_37 - 76 3....

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