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This book presents collective works published in the recent Special Issue (SI) entitled "Multivariate Approximation for Solving ODE and PDE". These papers describe the different approaches and related objectives in the field of multivariate approximation. The articles in fact present specific contents of numerical methods for the analysis of the approximation, as well as the study of ordinary differential equations (for example oscillating with delay) or that of partial differential equations of the fractional order, but all linked by the objective to present analytical or numerical techniques for the simplification of the study of problems involving relationships that are not immediately computable, thus allowing to establish a connection between different fields of mathematical analysis and numerical analysis through different points of view and investigation. The present contents, therefore, describe the multivariate approximation theory, which is today an increasingly active research area that deals with a multitude of problems in a wide field of research. This book brings together a collection of inter-/multi-disciplinary works applied to many areas of applied mathematics in a coherent manner.

nonlinear equations --- iteration methods --- one-point methods --- order of convergence --- oscillatory solutions --- nonoscillatory solutions --- second-order --- neutral differential equations --- multiple roots --- optimal convergence --- bivariate function --- divided difference --- inverse difference --- blending difference --- continued fraction --- Thiele–Newton’s expansion --- Viscovatov-like algorithm --- symmetric duality --- non-differentiable --- (G,αf)-invexity/(G,αf)-pseudoinvexity --- (G,αf)-bonvexity/(G,αf)-pseudobonvexity --- duality --- support function --- nondifferentiable --- strictly pseudo (V,α,ρ,d)-type-I --- unified dual --- efficient solutions --- Iyengar inequality --- right and left generalized fractional derivatives --- iterated generalized fractional derivatives --- generalized fractional Taylor’s formulae --- poisson equation --- domain decomposition --- asymmetric iterative schemes --- group explicit --- parallel computation --- even-order differential equations --- neutral delay --- oscillation --- Hilbert transform --- Hadamard transform --- hypersingular integral --- Bernstein polynomials --- Boolean sum --- simultaneous approximation --- equidistant nodes --- fourth-order --- delay differential equations --- riccati transformation --- parameter estimation --- physical modelling --- oblique decomposition --- least-squares