INDEX solver

Density, g/mL Refractive index Melting point,°C Boiling point,°C Flash point,°C Solubility in parts solver... 

Using the model described here, the anisotropic stress field inside the silicon ridge waveguides shown in Figure 9 were calculated. Applying Equation 1 to evaluate the anisotropic index of refraction, the FEM mode solver was used to determine the effective index values Nje and Njm for the... 

Pantelides, C., Keeping, B., Bernier, J., Gautreau, C. Open interface specification Numerical solvers. Technical Report CO-NUMR-EL-03, The CAPE-OPEN Laboratories Network, CO-LaN (1999), http //www.colaii.org/ index-33.html... 

You can interrupt Solver by pressing the Escape button on your keyboard. This will abort the calculation being done at that time, and show the previous result calculated by Solver. Help => Answer Wizard contains a large number of useful comments and hints concerning Solver, as does the Answer Wizard Index. Consult these if you want to knowmore about it. 

Before finishing this section, we would like to discuss the practical aspects of mixing index calculations. The method requires utilization of the species transport equation along with a flow solver, which presently exists... 

A characteristic of DAEs besides their form is their differentiation index [32]. For a definition and an example see Appendix C. It is an indicator for the problems to be encountered with the numerical solution of a set of DAEs. Systems of index > 1 are usually called higher index DAEs and the higher the index the more severe numerical difficulties can be. As the mathematical description of problems in various disciplines often leads to DAE system, they have been a research subject for more than two decades. A large body of publications and a number software programs for their numerical solution have emerged. DAE systems of index 1 can be safely numerically computed by means of the backward differentiation formula (BDF) [33, 34] implemented in solvers such as the well known and widely used DASSL code [35]. 

The DAE form (2.22) is known as Hessenberg index-2 form. This form can be directly numerically solved by the DASKP 3.0 solver [43, 44] or the MEBDFI [45] solver available in Maple [46], Both solvers use the BDF method. ... 

If the dynamic behaviour of a system can be described by a switched LTI system, a linear implicit DAE system can be derived from the bond graph. The entries of its matrices depend on the discrete switch states. As long as no structural changes occur, i.e. no residual sinks are switched on, the DAE system is of index <1. For system modes in which residuals sinks are switched on, the DAE system is of index 2. There are solvers available for its direct numerical computation that are based on the BDF-method. An alternative may be to perform a DEVS simulation that uses quantised based integration. 

We will solve for each of the species flow rates and the pressure profile. First, we define all of our constants in Mathcad. We include one additional value, Num, which is the number of integrating steps between the start and end points. Please note that the authors do not recommend using the built-in units when woricing with ODE solvers. Next, we create a matrix of initial values for each of our equations and a matrix of the differential equations. Mathcad indexes from zero, and therefore, our first equation is fg. To solve the system, we choose rkfixed and assign the result to fn. Fn is now a matrix of our solution set that we can plot. Alternatively, we can see our matrix result by typing fn=. The final workspace is shown as follows. 

Soares, R. de P. and Secchi, A.R., 2002, Direct Initialization and Solution of High-Index DAE Systems with Low-Index DAE solvers. Comp. Chem. Engrg (submitted 2002). 

A few other bookkeeping sections in the code convert the input solution array from an x-y labeled two index matrix into a single column array if needed on lines 454 through 459 and a final loop converts the single column solution array into a j,i two index matrix of solution values on lines 486 through 488. The type of solution desired may be specified as a table of values in order to pass additional parameters to the PDE solver. If a table is specified for the typsola parameter, two additional parameters, rx and ry, can be extracted from the input list as seen on line 444. For a direct sparse matrix solution with the SPM parameter these are not used. For the COE and SOR methods, this feature can be used to specify a spectral radius value with only the rx parameter used. For the ADI method these two values can be used to specify wx and wy parameters. In all cases, default values of these parameters are available, if values are not input to the various functions. 

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