Chemical Engineering Hand Written_Notes_Part_75

Chemical Engineering Hand Written_Notes_Part_75 - 152 4....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
152 4. ODE-IVPS AND RELATED NUMERICAL SCHEMES Substitution of equations (3.77),(3.78) and (3.80) into (3.71) gives what is known as the exactness constraints for the algorithm as m X j =0 a j,n ( h ) j = p X i =0 α i " m X j =0 a j,n ( ih ) j # + h p X i = 1 β i " m X j =1 ja j,n ( ih ) j 1 # = Ã p X i =0 α i ! a 0 ,n + Ã p X i =0 ( i ) α i + p X i = 1 ( i ) 0 β i ! a 1 ,n h + ... ... + Ã p X i =0 ( i ) m α i + m p X i = 1 ( i ) m 1 β i ! a m,n h m (3.82) Because we would like (3.82) to hold independently of any stepsize, we obtain the following equations (constraints) by equating like powers of h . p X i =0 α i =1 ; ( j =0) (3.83) p X i =0 ( i ) j α i + j p X i = 1 ( i ) j 1 β i =1; ( j =1 , 2 , ....... , m ) (3.84) Note :( i ) j =1 when i = j =0 Thus, equations (3.88-3.90) gives m +1 constraints and the number of variables are 2 p +3 ,name ly α 0 , ....... α p 1 0 , ....... β p . Any choice of these constants
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 2

Chemical Engineering Hand Written_Notes_Part_75 - 152 4....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online