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...
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...
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 ...
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...
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.
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}{-...
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...
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...
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...
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...
