Lect_7_-_Numerical_solution_-_part_1

Lect_7_-_Numerical_solution_-_part_1 - Numerical Solution...

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Numerical Solution (function with single variable) Prof. Ir. Dr. Mohd Sobri Takriff ept. of Chemical & Process ngineering Dept. of Chemical & Process Engineering Universiti Kebangsaan Malaysia
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Review Process model is defined as a set of equations that allows us to predict the behavior of a system most of the process model is in the form f ifferential quations of differential equations
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Ex – process model for heat & mass balance for gas reaction system F F dt d V 0 0 C B 2 5 . 1 A 1 A 0 A 0 A C Vk 2 C Vk FC C F dt dC V  0 v P P C F   ZRT P M ) y 1 ( yM ZRT pM B A RT yP C A   RT P y 1 C B G V T FC T C F dt dT C V p 0 p 0 p
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Review Differential Equation an equation containing the derivatives or differentials of one or more dependent variables ith respect to one or more independent with respect to one or more independent variables. Differential equations are classified according to their Type , Order and Linearity .
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Review Classification by type ordinary differential equation- contains yq only ordinary derivatives of one or more dependent variables with respect to only a single independent variable, e.g. ; 5 y 2 dt dy 0 y 2 dx dy 5 dx y d 3 3
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Review Classification by type partial differential equations - contain the pq partial derivatives of one or more dependent variables with respect to two or more independent variable ; 0 y v y 2 x v t u 2 t u x u 2 2 2 2
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Review Classification by Order - The highest order of the derivatives is called the order of the equation third order ordinary differential equation 0 u 5 dx du 6 dx u d 5 3 3 fifth order partial differential equation 2 5 0 t u a x u 2 5
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Review Classification by linearity General form of a differential equation y n n 1 Linear differential equations are characterizes by           x g y x a dx dy x a dx y d x a dx y d x a n n n n 0 1 1 1 ..... the following properties The dependent variable and all of its derivatives are of the first order; i.e. the power of each term involving the dependent variables is 1. Each coefficients depends only on the independent variables.
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Review Classification by linearity Examples ; 0 y 2 dx dy ; , " 0 2 y y y 0 5 2 2 2 2 3 3 3 y dx dy x dx y d x dx y d x
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Review Classification by linearity Examples y d 2 Coefficient depend on the dependent variable 0 y 2 dx y 3 Power not 1 0 y y d x y d 2 2 2 3 dx dx 2 3
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xample Example F F dt d V 0 0 B 2 5 . 1 A 1 A 0 A 0 A C Vk 2 C Vk FC C F dt dC V ype?
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Lect_7_-_Numerical_solution_-_part_1 - Numerical Solution...

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