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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

We discuss an Adams-type predictor-corrector method for the numericalsolution of fractional differential equations. The method may be usedboth for linear and for nonlinear problems, and it may be extended tomulti-term equations (involving more than one differential operator)too.

https://ntrs.nasa.gov/api/citations/20020024453/downloads/20020024453.pdf

A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

Numerical Initial Value Problems in Ordinary Differential Equations

Advanced Mathematical Methods for Scientists and Engineers

A new algorithm for solving Toeplitz systems of equations

The application of certain difference schemes (box, trapezoidal, Euler and backward Euler) to the numerical solution of boundary value problems for nonlinear first order systems of ordinary differential equations with a singularity of the first kind is examined. The solution of the linear eigenvalue problem is also considered.

Difference Methods for Boundary Value Problems with a Singularity of the First Kind

Application of Compressive Sampling to Radio Astronomy I: Deconvolution

Compressive sampling is a new paradigm for sampling, based on sparseness of signals or signal representations. It is much less restrictive than Nyquist-Shannon sampling theory and thus explains and systematises the widespread experience that methods such as the H\"ogbom CLEAN can violate the Nyquist-Shannon sampling requirements. In this paper, a CS-based deconvolution method for extended sources is introduced. This method can reconstruct both point sources and extended sources (using the isotropic undecimated wavelet transform as a basis function for the reconstruction step). We compare this CS-based deconvolution method with two CLEAN-based deconvolution methods: the H\"ogbom CLEAN and the multiscale CLEAN. This new method shows the best performance in deconvolving extended sources for both uniform and natural weighting of the sampled visibilities. Both visual and numerical results of the comparison are provided.

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The application of compressive sampling to radio astronomy I: Deconvolution

The application of collocation methods based on piecewise polynomials to the numerical solution of boundary value problems for systems of ordinary differential equations with a singularity of the first kind is examined. The schemes are shown to be stable and convergent. Enhanced accuracy at the nodes for suitably chosen collocation points (superconvergence) is established for a class of important problems.

Frank de Hoog

Papers

A new algorithm for solving Toeplitz systems of equations

Difference Methods for Boundary Value Problems with a Singularity of the First Kind

Application of Compressive Sampling to Radio Astronomy I: Deconvolution

The application of compressive sampling to radio astronomy I: Deconvolution

Collocation Methods for Singular Boundary Value Problems