Chemical Engineering Hand Written_Notes_Part_80

Chemical Engineering Hand Written_Notes_Part_80 - 162 4....

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162 4. ODE-IVPS AND RELATED NUMERICAL SCHEMES Polynomial approximation based algorithms (Predictor-corrector type methods). In the end, we provide a brief introduction to the stability analysis of the numerical algorithms for solving ODE-IVPs. 6. Exercise (1) Express the following set of equations in the standard form dx/dt = Ax ; x (0) = x (0) and solve the resulting initial value problem analytically (a) Set 1 d 2 y/dt 2 +4 dy/dt +3 y =0; y (0) = 1; dy/dt =0 at t =0 (b) Set 2 d 3 y/dt 3 +6 d 2 y/dt 2 +11 dy/dt +6 y =0 y (0) = 1; dy/dt = d 2 y/dt 2 =0 at t =0 ; (c) Set 3 dy/dt +3 y + z =0; y (0) = 1 d 2 z/dt 2 +3 dz/dt +2 z =0 z (0) = 1; dz/dt =0 Compare the coe cients of the characteristic equation, i.e. det ( λI A )=0 , and those of the ODE(s) for the f rst two sets. Also, commen tuponthea symp to
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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.

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Chemical Engineering Hand Written_Notes_Part_80 - 162 4....

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