Numerical Simulation of Distributed Parameter Processes

Tiberiu Coloşi, Mihail Abrudean, Mihaela-Ligia Ungureşan, Vlad Mureşan

Numerical Simulation of Distributed Parameter Processes

Springer Verlag 2013, 340 pages

The monography “Numerical Simulation of Distributed Parameter Processes” defines, interprets and uses the “matrix of partial derivatives of the state vector (Mpdx)” with applications for the study of some common categories of engineering, of the processes with distributed and concentrated parameters. 

For such processes we mainly pursued the elaboration of a unified and systematic method for:

-The analogical modeling through (Mpdx);

-The numerical simulation through (Mpdx) and Taylor Series.

The book covers broad categories of processes, formed by systems of partial differential equations (PDE), including systems of ordinary differential equations (ODE), analogically modeled and numerically simulated by (Mpdx).

The book includes numerous applications specific for the Systems-Theory, based on (Mpdx), such as parallel, serial and with feed-back connections for the processes defined by PDE. For similar more complex processes based on (Mpdx), having PDE and ODE as components, we have developed control schemes with PID effects, for the propagation phenomena, in continuous media (spaces) or discontinuous ones (chemistry, power system, thermoenergetic, metallurgy) or in electro-mechanics (railway – traction) and so on.

The volume is structures on the following parts, respectively chapters: 


Chapter 1. Linear processes invariant in time

Chapter 2. Time varying linear processes

Chapter 3. Non-linear processes with lumped parameters


Chapter 4. Linear processes with distributed parameters

Chapter 5. Non-linear processes with distributed parameters

Chapter 6. Truncation errors of the operator matrix (Mpdx)


Chapter 7. Modeling and simulation examples of lumped parameters processes

Chapter 8. Modeling and simulation examples for distributed parameters processes

Chapter 9. Case studies for establishing the (Mpdx) matrix

Chapter 10. Partial  derivative  equations  in the Cartesian space

Chapter 11. Parallel, serial and with feed-back connection, for the processes modeled through PDE

Chapter 12. Control system with distributed and lumped parameters in the Cartesian space –cases studies

Chapter 13. Numerical simulation using partial  differential equations, for propagation and control in discontinuous structures processes

Appendix A1: Summary for (Mpdx) matrix

Appendix A2: Local-Iterative Linearization Method

Appendix A3: Regarding to the Convergence of the Local-Iterative Linearization Method

The work has a purely engineering nature and it has, as a target audience, extremely diverse applicative fields (propagation phenomena, diffusion, hydrodynamics, electro-mechanics) - where the use of (PDE) and (ODE) is justified - and for which the approximated solutions can assure a good compromise between the theoretical rigor and the relative errors cumulated in acceptable or negligible percentages.

                                                   The authors