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This e-book offers a strategy for the improvement and desktop implementation of dynamic versions for shipping technique platforms. instead of constructing the overall equations of delivery phenomena, it develops the equations required in particular for every new instance program. those equations are normally of 2 kinds: usual differential equations (ODEs) and partial differential equations (PDEs) for which Read more...
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Extra resources for Dynamic Modeling of Transport Process Systems
Sample text
6 Concluding Linear 51 Example We now consider the Fortran program for the numerical integration of eqs. 2. 1. C O M M O N / T / has been expanded to include two integer elements, NSTOP and NORUN, which are used in the following ways: (a) NSTOP is set to zero in the main program, DSS2S in Appendix 2a, at the beginning of each run. If the user then sets NSTOP to a nonzero value in subroutines INITAL, DERV, or PRINT, the current run is terminated in DSS2S and the next run is initiated if data remain to be read.
However, the procedures we are describing can be implemented using subroutine arguments with minor modifications, which will be illustrated in subsequent examples). 3. The integrator calls a user-written subroutine, call it DERV, to evaluate the derivative vector at point i (/ = 0 for the first call to DERV). The integrator then takes a step along the solution using eq. 7) (or, in general, using the stepping formula of the integration algorithm, which may require the derivative at several points between i and i + 1) to produce the solution vector at i + 1.
One way to reduce these local and total errors is to reduce the 26 2. Basic Concepts in the Numerical Integration of Ordinary Differential Equations h(oo) t=0 Δί t Fig. 2 Approximation of an O D E solution by Euler's method. integration step, Δί. Another way is to use an algorithm that does not have the inherent limitation in accuracy of Euler's method, that is, that does better than approximate the solution with linear segments based on the ODE derivative evaluated at the base point i. Therefore we might consider an algorithm that uses the derivative at the base point (dhjdt) and at the advanced point (dhi+l/dt).
