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10.34 Numerical Methods Applied to Chemical Engineering Fall 2012 Homework # 6: Differential -Algebraic Equations, Boundary Value Problems Date : 10/24/2012 Due : 10/31/2012 Problem 1 (20 points) Consider the case of liquid level control for the tank in Figure 1. The tank has one input flow 1 q and one output flow 2 q (volumetric flow rates) . The level of the liquid is h and the t ank has a Guido Buzzi-Ferraris and Flavio Manenti, Differential and Differential-Algebraic Systems for the Chemical Engineer: Solving Numerical Problems, WILEY-VCH, Weinheim, Germany, to be published

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A system of ordinary differential equations (ODE) has the following characteristics: All of the equations are ordinary differential equations. Each equation is the derivative of a dependent variable with respect to one independent variable, usually time. Solvability of systems: If a set of n independent equations has n unknowns, then the system has a finite (possibly 0) number of solutions. If a set of n independent equations has less than n unknowns then the system has an infinite number of solutions.

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## Partial Differential Equation Analysis in Biomedical

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Differential and Differential-Algebraic Systems for the Chemical Engineer: Solving Numerical Problems . By Guido Buzzi-Ferraris and Flavio Manenti. Cite . BibTex; Full citation; Abstract. Engineers and other applied scientists are frequently faced with models of complex systems for which no rigorous mathematical solution can be calculated. To predict and calculate the behaviour of such systems A variety of systems encountered in chemical engineering are traditionally viewed as exhibiting hybrid continuous and discrete behavior. In many cases such discrete behavior is nonsmooth (i.e. continuous but nondifferentiable) rather than discontinuous, and is appropriately modeled by nonsmooth DAEs. A computationally relevant theory of nonsmooth DAEs (i.e. well-posedness and sensitivity

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A variety of systems encountered in chemical engineering are traditionally viewed as exhibiting hybrid continuous and discrete behavior. In many cases such discrete behavior is nonsmooth (i.e. continuous but nondifferentiable) rather than discontinuous, and is appropriately modeled by nonsmooth DAEs. A computationally relevant theory of nonsmooth DAEs (i.e. well-posedness and sensitivity DIfferential and differential-algebraic systems for the chemical engineer: solving numerical problems

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