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:
Ist PART: PROCESSES WITH LUMPED PARAMETERS
Chapter 1. Linear processes invariant in time
Chapter 2. Time varying linear processes
Chapter 3. Non-linear processes with lumped parameters
IInd PART: PROCESSES WITH DISTRIBUTED 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)
IIIrd PART: SIMULATION EXAMPLES
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.