Mathematical and Computational Methods for Modelling, Approximation and Simulation

This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models. The book includes nine contributions, mostly related to quasi-interpolation. This is a topic that continues to register a high level of interest, both for those working in the field of approximation theory and for those interested in its use in a practical context. Two chapters address the construction of quasi-interpolants, and three others focus on the use of quasi-interpolation in solving integral equations. The remaining four concern a problem related to the heat diffusion equation, new results on the notion of convexity in probabilistic metric spaces (which are applied to the study of the existence and uniqueness of the solution of a Volterra equation), the use of smoothing splines to address an economic problem and, finally, the analysis of poverty measures, which is a topic of increased interest to society. The book is addressed to researchers interested in Applied Mathematics, with particular reference to the aforementioned topics.

Auteur

Domingo Barrera is a Full Professor of Applied Mathematics at the Department of Applied Mathematics of the University of Granada. His current main research line is spline quasi-interpolation and its application to the numerical solution of integral equations and in the use of advanced mathematical techniques for the extraction of parameters in the modelling of nanoelectronic devices and the study of the functional quality of digital models of terrain elevations in engineering.

Sara Remogna is a Professor of Numerical Analysis at the University of Torino (Italy). Her research interests include univariate and multivariate spline approximation, numerical methods for computer-aided geometric design, and numerical methods for the solution of differential and integral problems based on spline approximation.

Driss Sbibih is a Full Professor of Approximation and Numerical Analysis at the University Mohammed First in Morocco. His research interests are approximation theory by spline functions, computer graphics and numerical analysis. He has a long experience in international cooperation, especially with universities in Spain, France and Italy.

Contenu

Part I Plenary Lectures.- 1 S. De Marchi, Mapped polynomials and discontinuous kernels for Runge and Gibbs phenomena.- 2 P. Pedregal, Steady systems of PDEs. Two examples from applications.- 3 C. Bracco et al., THB-spline approximations for turbine blade design with local B-spline approximations.- Part II Contributed papers.- 4 A. Abbadi and M. J. Ibáñez, A progressive construction of univariate spline quasi-interpolants on uniform partitions.- 5 C. Allouch et al., Richardson extrapolation of Nyström method associated with a sextic spline quasi-interpolant.- 6 A. Bellour et al., Superconvergent methods based on cubic splines for solving linear integral equations.- 7 R. Korikache and L. Paquet, The completely discretized problem of the dual mixed formulation for the heat diffusion equation in a polygonal domain by the Crank-Nicolson scheme in time.- 8 R. Akhrif et al., Economic statistical splicing data using smoothing quadratic splines.- 9 A. Mbarki and R. Oubrahim, Some properties of convexity structure and applications in b-Menger spaces.- 10 A. Rahouti et al., A Super-superconvergent Cubic Spline Quasi-interpolant.- 11 M. Illescas-Manzano et al., Calibration adjustment for dealing with nonresponse in the estimation of poverty measures.- 12 D. Barrera et al., Numerical methods based on spline quasi-interpolating operators for Hammerstein integral equations.