Aussal, Matthieu Haddar, Houssem Montanelli, Hadrien

We present algorithms for computing weakly singular and near-singular integrals arising when solving the 3D Helmholtz equation with high-order boundary elements. These are based on the computation of the preimage of the singularity in the reference element's space using Newton's method, singularity subtraction, the continuation approach, and transp...

Sidi, Avram
Published in
Calcolo

We consider the numerical computation of I[f]=∫=abf(x)dx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I[f]=\int \!\!\!\!\!=^b_a f(x)\,dx$$\end{document}, the Hadamard...

Buchheit, Andreas A. Keßler, Torsten
Published in
Journal of Scientific Computing

We develop a new expansion for representing singular sums in terms of integrals and vice versa. This method provides a powerful tool for the efficient computation of large singular sums that appear in long-range interacting systems in condensed matter and quantum physics. It also offers a generalised trapezoidal rule for the precise computation of ...

Eftekhari, Tahereh Rashidinia, Jalil Maleknejad, Khosrow
Published in
Advances in Difference Equations

The purpose of this paper is to provide sufficient conditions for the local and global existence of solutions for the general nonlinear distributed-order fractional differential equations in the time domain. Also, we provide sufficient conditions for the uniqueness of the solutions. Furthermore, we use operational matrices for the fractional integr...

Latif, Muhammad Amer
Published in
Advances in Difference Equations

In this paper, we obtain new Hermite–Hadamard-type inequalities for r-convex and geometrically convex functions and, additionally, some new Hermite–Hadamard-type inequalities by using the Hölder–İşcan integral inequality and an improved power-mean inequality.

Sidi, Avram
Published in
Calcolo

In a recent work, we developed three new compact numerical quadrature formulas for finite-range periodic supersingular integrals I[f]=∫=abf(x)dx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-...

Khosravian-Arab, Hassan Eslahchi, Mohammad Reza
Published in
Fractional Calculus and Applied Analysis

This paper presents two new classes of Müntz functions which are called Jacobi-Müntz functions of the first and second types. These newly generated functions satisfy in two self-adjoint fractional Sturm-Liouville problems and thus they have some spectral properties such as: orthogonality, completeness, three-term recurrence relations and so on. Wit...

Jaramillo, Gabriela Cappanera, Loic Ward, Cory
Published in
Journal of Scientific Computing

In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, ν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odds...

Sidi, Avram
Published in
Calcolo

We consider the numerical computation of finite-range singular integrals that are defined in the sense of Hadamard Finite Part, assuming that g∈C∞[a,b]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidema...

Al-Shomrani, M. M. Abdelkawy, M. A.
Published in
Advances in Difference Equations

In this paper, we present a numerical simulation to study a fractional-order differential system of a glioblastoma multiforme and immune system. This numerical simulation is based on spectral collocation method for tackling the fractional-order differential system of a glioblastoma multiforme and immune system. We introduce new shifted fractional-o...