By Alkis Constantinides, Navid Mostoufi

ISBN-10: 0130138517

ISBN-13: 9780130138514

Presents a whole advisor to numerical equipment in chemical engineering and takes complete good thing about MATLAB's robust calculation setting. includes numerous examples utilizing normal MATLAB capabilities that enforce the tactic and will even be utilized to many different difficulties within the comparable type. CD-ROM incorporated. DLC: Numerical analysis--Data processing.

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Extra info for Numerical Methods for Chemical Engineers with MatLab Applications

Sample text

Therefore, the general iterative formula for the Wegstein method is The Wegstein method converges, even under conditions in which the method of x = g (1) does not. Moreover, it accelerates the convergence when the successive substitution method is stable (Fig. 36). 3 The Wegstein method. This technique is based on linear interpolation between two points on the function that have been found by a scan to lie on either side of a root. For example, x, and x2in Fig. 5 The Method of Linear Interpolation (Method of False Position) 11 positions on opposite sides of the root x' of the nonlinear functionf ( x ) .

All the roots of the transfer function are evaluated at each step of the bisection search. 4. The roots are checked for positive real part. The range of Kc, over which the change from negative to positive roots occurs, is retained. 5. Steps 2-4 are repeated until successive values of Kc change by less than a convergence criterion, E. m calculates all roots of a polynomial by the Newton-Raphson method with synthetic division as described in the Method of Solution. Unlike other functions employing the Newton-Raphson method, this function does not need a starting value as one of the input arguments.

A) Convergence. (b) Divergence. 456) will he determined by exploring both values of x,:, and x,, and determining which one results in the function f(x,++,) or f(xn-+,) being closer to zero. An alternative to the above exploration will be to treat Eq. 43) as another nonlinear equation in Ax and to apply the Newton-Raphson method for its solution: F(Ax) = f"(xl) (Ax)' 2! 46) where Two nested Newton-Raphson algorithms would have to he programmed together as follows: 1. 2. 3. 4. 5. Assume a value of x,.