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Unformatted text preview: 130 4. ODE-IVPS AND RELATED NUMERICAL SCHEMES where x R m and F ( x ) is a m 1 function vector. Introducing a parameter such that (0 1) , we de f ne (1.18) F ( x ( )) = (1 ) F ( x (0) ) where x (0) represents some arbitrary initial guess. Obviously, at = 1 we have F ( x ) = . Di f erentiating w.r.t. and rearranging, we get d x d = [ F x ] 1 F ( x (0) ) (1.19) x (0) = x (0) (1.20) Integrating above ODE-IVPs from = 0 to = 1 produces the solution of nonlinear the equations at = 1 . 1.3. Solutions of Parabolic / Hyperbolic PDEs. 1.3.1. Finite Di f erence Method. Use of f nite di f erence method to solve par- abolic or hyperbolic equations with f nite spatial boundaries results in set of coupled linear / nonlinear ODE-IVPs. Example 52 . Consider the ODE-BVP describing steady state con- ditions in a tubular reactor with axial mixing (TRAM) in which an irreversible 2nd order reaction is carried out....
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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.
- Fall '11
- Chemical Engineering