Chemical Engineering Hand Written_Notes_Part_65

Chemical Engineering Hand Written_Notes_Part_65 - 132 4....

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132 4. ODE-IVPS AND RELATED NUMERICAL SCHEMES 1.3.2. Orthogonal Collocation Method. Example 55 . Consider the ODE-BVP describing steady state conditions in a tubular reactor with axial mixing (TRAM) given in the above section. Using method of orthogonal collocation with m internal collocation points, we get dC i ( t ) dt = 1 Pe h £ t ( i ) ¤ T C i h ¡ s ( i ) ¢ T C i DaC 2 i i =1 , 2 , 3 ,...m h £ t (0) ¤ T C i = ( C 0 ( t ) 1) h £ t ( m +1) ¤ T C i =0 where the matrices £ t ( i ) ¤ and ¡ s ( i ) ¢ represent row vectors of matrices T and S, as de f ned in the Section 5 (example 6) of lecture notes on linear algebraic equations and related numerical scheme. . Here, C i ( t ) represents concentration at the i’th collocation point. The above set of ODEs, together with initial conditions, C 1 (0) = C 2 (0) = ..... = C m +1 (0) = 0 de f nes an ODE-IVP of type (1.16). 1.4. Solution of ODE-BVP: Shooting Method. By this approach, we reduce the 2nd or higher order ODE-BVP to a set of f rst order ODE’s.
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Chemical Engineering Hand Written_Notes_Part_65 - 132 4....

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