**About the Editor**

**Clemente Cesarano** is an associate professor of Numerical Analysis and the director of the Section of Mathematics—Uninettuno University, Rome, Italy; he is the coordinator of the doctoral college in Technological Innovation Engineering, coordinator of the Section of Mathematics, vicedean of the Faculty of Engineering, president of the Degree Course in Management Engineering, director of the Master in Project Management Techniques, and a coordinator of the Master in Applied and Industrial Mathematics. He is also a member of the Research Project "Modeling and Simulation of the Fractionary and Medical Center", Complutense University of Madrid (Spain), and the head of the national group from 2015, member of the Research Project (Serbian Ministry of Education and Science) "Approximation of Integral and Differential Operators and Applications", University of Belgrade (Serbia) and coordinator of the national group since 2011), a member of the Doctoral College in Mathematics at the Department of Mathematics of the University of Mazandaran (Iran), expert (Reprise) at the Ministry of Education, University and Research, for the ERC sectors: Analysis, Operator Algebras and Functional Analysis, and Numerical Analysis. Clemente Cesarano is an honorary fellow of the Australian Institute of High Energetic Materials, affiliated with the National Institute of High Mathematics (INdAM), as well as with the International Research Center for the "Mathematics & Mechanics of Complex Systems" (MEMOCS)—University of L'Aquila, associate of the CNR at the Institute of Complex Systems (ISC), affiliated with the "Research Italian Network on Approximation (RITA)" as the head of the Uninettuno office. Finally, he is a member of the UMI and the SIMAI

## **Preface to "Multivariate Approximation for solving ODE and PDE"**

Multivariate approximation is an extension of approximation theory and approximation algorithms. In general, approximations can be provided via interpolation, as approximation/ polynomials' interpolation and approximation/interpolation with radial basis functions or more in general, with kernel functions. In this book, we have covered the field through spectral problems, exponential integrators for ODE systems, and some applications for the numerical solution of evolutionary PDE, also discretized, by using the concepts and the related formalism of special functions and orthogonal polynomials, which represent a powerful tool to simplify computation. Since the theory of multivariate approximation meets different branches of mathematics and is applied in various areas such as physics, engineering, and computational mechanics, this book contains a large variety of contributions.

> **Clemente Cesarano** *Editor*
