**Workshop**

**'Numerical Simulation of Evolutionary Processes'**

14 – 17 January 2014

*C.N.R., Area della Ricerca, via Amendola 122/D (first floor, **meeting room**), Bari*

*ITALY*

Two topics of the greatest interest, related to a fractional differential equations and the study of population dynamics, will be the focus of the workshop activities.

- The fractional differential equations are a natural extension of the classical differential equations and are used in many application fields, such as, for example, biology, chemistry , mechanical engineering. In particular, will be analyzed Fractional differential equations for real-life problems such as the SIRC model fractional and model for influenza A. It is very important to find for these problems an efficient numerical solution, parallel methods of the weighed differences finite schemes will be analyzed. We also analyze in detail the differential equations of fractional variable order and some techniques for their numerical solution .
- The mathematical modeling of population dynamics plays a important role in the study of biodiversity. The spatial dimension plays a decisive role in the study of evolutionary processes of the species. The development of algorithms and codes for the numerical simulation of mathematical models that describe the spatially explicit dynamics using approaches based on differential equations and models based on individuals (Individual Based Models) are topics of great interest in all those applications that aim to protect the environment and species. We propose the most recent results related to the issues related to the mathematical description of the phenomena of habitat fragmentation by metapopulation models, persistence and control of the spread of populations in dynamic environments, and thus we will stimulate research into the development of efficient algorithms able to give mathematical foundation to current systems decision support that operate in the environmental sector.

The workshop is organized as part of the Executive Protocol "Numerical Simulation of real life problems" between the University of Bari, Department of Mathematics and the University of Cairo, Department of Mathematics, as part of the CNR research funded activity "Spatially implicit and explicit models for cyclic metapopulation dynamics", as part of the activity of The PHD program in Mathematics of the University of Bari in collaboaration with CNR, and as part of the activity of the INDAM unit of Bari. Space for scientific discussions and research joint activity is considered.

**Plenary Speakers:**

Prof. Nasser Sweilam, Director of the Department of Mathematics, University of Cairo (Egypt)

Prof. Marcus R. Garvie, Department of Mathematics and Statistics, University of Guelph, (Canada)

Dr. Abdelhameed M. Nagy, Department of Mathematics, University of Benha (Egypt)

Dr. Francesco Giannino, Dipartimento di Ingegneria Agraria e Agronomia del Territorio, Universita' degli Studi di Napoli Federico II (Italy)

**Sponsored by:**

Istituto per Applicazioni del Calcolo "M.Picone", CNR, Bari, Italy

Dipartimento di Matematica, Università di Bari, Italy,

GNCS (Gruppo Nazionale per il Calcolo Scientifico).

**Organizing and Scientific Committee**:

Fasma Diele, Carmela Marangi, Francesca Mazzia

**PRELIMINARY SCIENTIFIC PROGRAM**

**Tuesday, January** 14th, 2014

14:55 – 15:00 *Opening Address* by F. Mazzia

15:00 – 16:00 N. Sweilam:

* On the fractional order differential equations for real life models. *

* *16:00 – 16:15 coffee break

16:15 – 17:15 A. M. Nagy:

* Variable Order Fractional Differential Equations, theory and applications*

* * 17:15 – 17:40 F. Mazzia

Numerical Solution of Initial and Boundary Value Problems in the open source software R

**Wednesday,** **January** 15th, 2014

9:30 – 10.30 Marcus R. Garvie:

*Fully spatially structured metapopulation models for predator-prey dynamics.*

10:30 – 10:45 coffe break

10:45 – 11.45 * *Francesco Giannino:

*Individual-based modeling approach to population dynamics*

11:45 – 12:10 S. Longo

Simple models for the emergence of homochiral molecules and species in Astrobiology

12:10 – 12:35 D. Lacitignola

Spatio-temporal organization in a reaction-diffusion model for alloy electrodeposition. Part I: theoretical issues

12:35 – 13:00 I. Sgura

**Thursday ,**

**January**16th, 2014

9:30 – 9.55 L. Brugnano

Recent advances in numerical methods for conservative problems

9:55 – 10.20 F. Iavernaro

Energy conservation methods for Hamiltonian Boundary Value Problems

10:20 – 10:45 F. Diele

10:45 – 11:05 F. Notarnicola

11:05 – 11:15 coffee break

11:15 – 11:40 L. Aceto

Fractional Generalized Adams Methods for FDEs

11:40 – 12:05 P. Novati

On the construction of k-step methods for Fractional Differential Equations

12:05 – 12:35 R. Garrappa

Exponential integrators for fractional differential equations

12:35 – 12:55 A. Martiradonna

Numerical simulation of fish population dynamics using R.

12:55 – 13:00 *Concluding Address by C. Marangi*

**Friday,** **January** 17th, 2014

8.30 -13:00 Escursion Bosco di Acquatetta 17th January

13:30 Social lunch

**WARNINGS**

All other contributed communications are by invitation only. No registration fee is required. The organization will cover only the expences for the guided visit to Alta Murgia Park (up to a maximum of 30 partecipants). However, the costs for reaching the Park will be covered by the partecipants.