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Full-Text Articles in Physical Sciences and Mathematics
Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Ashley Montiforte
Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Ashley Montiforte
Master's Theses
Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.
Survey Of Results On The Schrodinger Operator With Inverse Square Potential, Richardson Saint Bonheur
Survey Of Results On The Schrodinger Operator With Inverse Square Potential, Richardson Saint Bonheur
Electronic Theses and Dissertations
In this paper we present a survey of results on the Schrodinger operator with Inverse ¨ Square potential, La= −∆ + a/|x|^2 , a ≥ −( d−2/2 )^2. We briefly discuss the long-time behavior of solutions to the inter-critical focusing NLS with an inverse square potential(proof not provided). Later we present spectral multiplier theorems for the operator. For the case when a ≥ 0, we present the multiplier theorem from Hebisch [12]. The case when 0 > a ≥ −( d−2/2 )^2 was explored in [1], and their proof will be presented for completeness. No improvements on the sharpness …