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.