Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

We introduce a fast convolution-based method (FCBM) for solving linear and a certain class
of nonlinear peridynamic (PD) transient diffusion problems in 1D, 2D, and 3D. The method …

We review recent advances in algorithms for quadrature, transforms, differential equations
and singular integral equations using orthogonal polynomials. Quadrature based on …

We introduce an efficient boundary-adapted spectral method for peridynamic transient
diffusion problems with arbitrary boundary conditions. The spectral approach transforms the …

This paper presents a method for accurate and efficient computations on scalar, vector and
tensor fields in three-dimensional spherical polar coordinates. The method uses spin …

We investigate a spectral Galerkin method for the two-dimensional fractional diffusion-
reaction equations on a disk. We first prove regularity estimates of solutions in the weighted …

Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are
presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace …

We introduce a least-squares Fourier frame method for solving nonlocal diffusion models
with Dirichlet volume constraint on arbitrary domains. The mathematical structure of a frame …

Many interesting fluid phenomena exist on radial domains. Soap bubbles [Hill and
Henderson 2016; Huang et al. 2020; Yang et al. 2019] and planetary flows [Stam 2003; …

This paper explores a non-linear, non-local model describing the evolution of a single
species. We investigate scenarios where the spatial domain is either an arbitrary bounded …