Chemical Engineering Hand Written_Notes_Part_115

Chemical Engineering Hand Written_Notes_Part_115 - 232...

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5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES (10.59) v ( n ) ( z )= N n ( z )= z z n 1 z ; z n 1 z z n 0 Elsewhere Introduction of these trial functions allows us to express the approximate solu- tion as (10.60) b u ( z )= b u 0 v (0) ( z )+ ...... + b u n v ( n ) ( z ) and now we can work with b u = h b u 0 b u 2 ... b u n i T as unknowns. The optimum parameters b u canbecomputedbyso lv ingequat ion (10.61) A b u b = 0 where (10.62) ( A ) ij = ¿ dv ( i ) dz , dv ( j ) dz À and dv ( i ) dz = ( 1 / z on interval left of z i 1 / z on interval right of z i ) If intervals do not overlap,then (10.63) ¿ dv ( i ) dz , dv ( j ) dz À =0 The intervals overlap when (10.64) i = j : ¿ dv ( i ) dz , dv ( i ) dz À = z i Z z i 1 (1 / z ) 2 dz + z i Z z i 1 ( 1 / z ) 2 dz =2 / z or i = j +1: ¿ dv ( i ) dz , dv ( i 1) dz À = z i Z z i 1 (1 / z ) . ( 1 / z ) dz = 1 /
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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_115 - 232...

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