We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form 0D t u+ ∑d i=1[cli aiD 2μi xi u+ cri xiD 2μi bi u] +γ u = ∑d j=1[ κlj ajD 2νj xj u+κrj xjD 2νj bj u] +f , where 2τ ∈ (0, 2), 2μj ∈ (0, 1) and 2νj ∈ (1, 2), in a (1 +d)-dimensional space-time hypercube, d = 1, 2, 3, · · · ,...

This work proposes a windowed least-squares (WLS) approach for model reduction of dynamical systems. The proposed sequentially minimizes the time-continuous full-order-model residual within low-dimensional space–time trial subspace over time windows. comprises generalization existing approaches, as particular instances methodology recover Galerkin, Petrov–Galerkin (LSPG), and LSPG projection. I...