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04/20/2023
A class of mesh-free algorithms for some problems arising in finance and machine learning
We introduce a numerical methodology, referred to as the transport-based...
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12/26/2020
A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar tra
We develop a new finite volume method using unstructured mesh-vertex gri...
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11/15/2020
Well-balanced algorithms for relativistic fluids on a Schwarzschild background
We design well-balanced numerical algorithms with first-, second-, and t...
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07/17/2020
Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts
We study nonlinear hyperbolic conservation laws with non-convex flux and...
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05/27/2020
A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes
We consider a class of Fuchsian equations that, for instance, describes ...
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12/31/2019
Asymptotic structure of cosmological fluid flows in one and two space dimensions: a numerical study
We consider an isothermal compressible fluid evolving on a cosmological ...
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12/07/2019
Augmented hyperbolic models with diffusive-dispersive shocks
Given a first-order nonlinear hyperbolic system of conservation laws end...
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11/17/2019
Asymptotic structure of cosmological Burgers flows in one and two space dimensions: a numerical study
We study the cosmological Burgers model, as we call it, which is a nonli...
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11/03/2019
The Transport-based Mesh-free Method (TMM) and its applications in finance: a review
We review a numerical technique, referred to as the Transport-based Mesh...
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11/03/2019