The Wiener–Hopf technique, its generalizations and applications: constructive and approximate methods
This paper reviews the modern state of the Wiener–Hopf factorization method and its
generalizations. The main constructive results for matrix Wiener–Hopf problems are …
generalizations. The main constructive results for matrix Wiener–Hopf problems are …
[图书][B] Riemann–Hilbert problems, their numerical solution, and the computation of nonlinear special functions
This book grew out of the collaboration of the authors, which began in the Spring of 2010,
and the first author's PhD dissertation. The second author developed much of the theory in …
and the first author's PhD dissertation. The second author developed much of the theory in …
A Bayesian view on the Hilbert transform and the Kramers-Kronig transform of electrochemical impedance data: Probabilistic estimates and quality scores
Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental
tools in electrochemistry and has applications ranging from energy storage and power …
tools in electrochemistry and has applications ranging from energy storage and power …
Fast algorithms using orthogonal polynomials
We review recent advances in algorithms for quadrature, transforms, differential equations
and singular integral equations using orthogonal polynomials. Quadrature based on …
and singular integral equations using orthogonal polynomials. Quadrature based on …
A practical framework for infinite-dimensional linear algebra
S Olver, A Townsend - 2014 First Workshop for High …, 2014 - ieeexplore.ieee.org
We describe a framework for solving a broad class of infinite-dimensional linear equations,
consisting of almost banded operators, which can be used to representing linear ordinary …
consisting of almost banded operators, which can be used to representing linear ordinary …
Numerical inverse scattering transform for the focusing and defocusing Kundu–Eckhaus equations
S Cui, Z Wang - Physica D: Nonlinear Phenomena, 2023 - Elsevier
In this paper, we develop the numerical inverse scattering transform (NIST) for the focusing
and defocusing Kundu–Eckhaus (KE) equations. The NIST consists of numerical direct …
and defocusing Kundu–Eckhaus (KE) equations. The NIST consists of numerical direct …
Numerical inverse scattering for the Korteweg–de Vries and modified Korteweg–de Vries equations
Recent advances in the numerical solution of Riemann–Hilbert problems allow for the
implementation of a Cauchy initial-value problem solver for the Korteweg–de Vries equation …
implementation of a Cauchy initial-value problem solver for the Korteweg–de Vries equation …
A general framework for solving Riemann–Hilbert problems numerically
S Olver - Numerische Mathematik, 2012 - Springer
A new, numerical framework for the approximation of solutions to matrix-valued Riemann–
Hilbert problems is developed, based on a recent method for the homogeneous Painlevé II …
Hilbert problems is developed, based on a recent method for the homogeneous Painlevé II …
Numerical inverse scattering for the focusing and defocusing nonlinear Schrödinger equations
We solve the focusing and defocusing nonlinear Schrödinger (NLS) equations numerically
by implementing the inverse scattering transform. The computation of the scattering data and …
by implementing the inverse scattering transform. The computation of the scattering data and …
A fast and well-conditioned spectral method for singular integral equations
RM Slevinsky, S Olver - Journal of Computational Physics, 2017 - Elsevier
We develop a spectral method for solving univariate singular integral equations over unions
of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the …
of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the …