Chemical Engineering Hand Written_Notes_Part_76

Chemical Engineering Hand Written_Notes_Part_76 - 154 4....

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154 4. ODE-IVPS AND RELATED NUMERICAL SCHEMES Using the other constraints, (3.98) 11 ... 1 0( 1) ... ( p ) ... ... ... ... 1) m 1 ... ( p ) m 1 β 0 β 1 ... β p = 1 /j 1 /j ... 1 /j Solving for the β 0 s , we can write the algorithm as (3.99) x ( n +1)= x ( n )+ h £ β 0 f ( n β 1 f ( n 1) + ....... + β p f ( n p ) ¤ Adam-Moulton Implicit Algorithms: Choose (3.100) p = m 2 (3.101) α 1 = α 2 = ....... = α p =0 For j = 0, we have (3.102) p X i =0 α i =1 ; α 0 Remaining m variables β 1 , ....... , β m 2 can be determined by solving (3.103) ... 1 1) ... ( p ) ... ... ... ... 1) m 1 ... ( p ) m 1 β 1 β 0 ... β p = 1 1 / 2 ... 1 /m The algorithm can be written as x ( n +1) = x ( n h " β 0 f ( n β 1 f ( n 1)+ ... + β p f ( n p )] + β 1 f ( n +1) # (3.104) = y n + 1 f [ x ( n ,t n +1 ] (3.105) where y ( n ) represents sum of all terms which are known from the past data.
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Chemical Engineering Hand Written_Notes_Part_76 - 154 4....

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