6 citations · 8 across the 7 of their papers we have counts for
7 papers
A sparse spectral method on a class of domains bounded by planar algebraic curves
Jiajie Yao, Marco Fasondini, Sheehan Olver
We develop a sparse spectral method for solving partial differential equations on a class of two-dimensional geometries bounded by algebraic curves. The numerical method uses gener…
Complex-plane singularity dynamics for blow up in a nonlinear heat equation: analysis and computation
M. Fasondini, J. R. King, J. A. C. Weideman
Blow-up solutions to a heat equation with spatial periodicity and a quadratic nonlinearity are studied through asymptotic analyses and a variety of numerical methods. The focus is…
Orthogonal polynomials on a class of planar algebraic curves
Marco Fasondini, Sheehan Olver, Yuan Xu
We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form in where and is a polynomial of arbitrary degree ,…
Blow up in a periodic semilinear heat equation
Marco Fasondini, John R. King, J. A. C. Weideman
Blow up in a one-dimensional semilinear heat equation is studied using a combination of numerical and analytical tools. The focus is on problems periodic in the space variable and…
The numerical solution of fractional integral equations via orthogonal polynomials in fractional powers
Tianyi Pu, Marco Fasondini
We present a spectral method for one-sided linear fractional integral equations on a closed interval that achieves exponentially fast convergence for a variety of equations, includ…
Orthogonal polynomials on planar cubic curves
Marco Fasondini, Sheehan Olver, Yuan Xu
Orthogonal polynomials in two variables on cubic curves are considered, including the case of elliptic curves. For an integral with respect to an appropriate weight function define…
Multidomain spectral method for the Gauss hypergeometric function
S. Crespo, M. Fasondini, C. Klein +2
We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius' m…