Chemical Engineering Hand Written_Notes_Part_48

# Chemical Engineering Hand Written_Notes_Part_48 - 98 3...

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

98 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES Gauss Seidel Iterations (6.7) x ( k +1) i = g i [ x ( k +1) 1 , ........ x ( k +1) i 1 ,x ( k ) i , ............ x ( k ) n ] i =1 , .......... , n Relaxation Method x ( k +1) i = x ( k ) i + ω [ g i ( x k ) x ( k ) i ] A popular method of this type is Wegstein iterations. Given initial guess vector x (0) x (1) i = g i ( x (0) ); ( i , ............. , n ) s ( k ) i = £ g i ( x ( k ) ) g i ( x ( k 1) ) ¤ h x ( k ) i x ( k 1) i i (6.8) ω ( k ) i = s ( k ) i h 1 s ( k ) i i x ( k +1) i = g i ( x ( k ) )+ ω ( k ) i [ x ( k ) i g i ( x ( k ) )] i , ......... , n The iterations can be terminated when (6.9) ° ° x ( k +1) x ( k ) ° ° Example 44 . Consider the ODE-BVP describing steady state conditions in a tubular reactor with axial mixing (TRAM) in which an irreversible 2nd order reaction is carried out. (6.10) 1 Pe d 2 C dz 2 dC dz DaC 2 =0 (0 z 1) dC dz = ( C 1) at z =0; (6.11) dC dz at z ; (6.12) Using method of f nite di f erence, we get following set of n +1 nonlinear algebraic equations 1 C i +1 2 C i + C i 1 ( z ) 2 C i +1 C i 1 2( z ) = DaC 2 i (6.13) or αC i +1 βC i + αC i 1 = DaC 2 i (6.14)

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

View Full Document
6. SOLVING NONLINEAR ALGEBRAIC EQUATIONS
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_48 - 98 3...

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

View Full Document
Ask a homework question - tutors are online