Numerical methods and modeling for chemical engineers - download pdf or read online

Read Online or Download Numerical methods and modeling for chemical engineers PDF

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Numerical methods and modeling for chemical engineers - download pdf or read online

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Note that the Euler formula is a one-step formula (k = 1) with b1 = 1. 51) and of the local solution zi + 1 about xi. In the case of a three-step formula Substituting values of z into this and expanding about xi gives where The Taylor’s series expansion of zi + 1 is and upon equating like power of h, we have 60 The solution of this set of linear , and the three-step Adams-Bashforth formula is equations is . 52) k = 3]. A difficulty with multistep methods is that they are not self-starting. 52) values for ui ui′, u′i − 1, and u′i − 2 are needed to compute ui + 1.

A difficulty with multistep methods is that they are not self-starting. 52) values for ui ui′, u′i − 1, and u′i − 2 are needed to compute ui + 1. The traditional technique for computing starting values has been to use Runge-Kutta formulas of the same accuracy since they only require u0 to get started. An alternative procedure, which turns out to be more efficient, is to use a sequence of s-step formulas with s = 1, 2, . . , k [6]. The computation is started with the one-step formulas in order to provide starting values for the two-step formula and so on.

2315. The large number of steps required for a “reasonably” accurate solution is a consequence of the first-order accuracy of the Euler method. 0463. 05 and the solution is stable and oscillatory. From the above table, when N = 20, the global error should oscillate if the propagation error is the dominant term in Eq. 21). 1. The data for N = 10 and N = 20 can be explained by examining Eq. 16. , term (B). 08. Therefore, As with N = 10, the global error is dominated by the term (A). Thus no oscillations in the global error are seen for N = 20.

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