Related papers: Generalized convolution quadrature based on the tr…
A coercivity property of temporal convolution operators is an essential tool in the analysis of time-dependent boundary integral equations and their space and time discretisations. It is known that this coercivity property is inherited by…
The acoustic wave equation is solved in time domain with a boundary element formulation. The time discretisation is performed with the generalised convolution quadrature method and for the spatial approximation standard lowest order…
This paper describes a trapezoidal quadrature method for the discretization of weakly singular, singular and hypersingular boundary integral operators with complex symmetric quadratic forms. Such integral operators naturally arise when…
In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is $(4-\alpha)$, where $\alpha…
The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…
We propose an efficient algorithm for the approximation of fractional integrals by using Runge--Kutta based convolution quadrature. The algorithm is based on a novel integral representation of the convolution weights and a special…
We present a method to rapidly approximate convolution quadrature (CQ) approximations, based on a piecewise polynomial interpolation of the Laplace domain operator, which we call the \emph{parsimonious} convolution quadrature method. For…
This paper shows that how to approximate general fuzzy number by using convolution method.
A high-order accurate quadrature rule for the discretization of boundary integral equations (BIEs) on closed smooth contours in the plane is introduced. This quadrature can be viewed as a hybrid of the spectral quadrature of Kress (1991)…
We consider a linear inhomogeneous fractional evolution equation which is obtained from a Cauchy problem by replacing its first-order time derivative with Caputo's fractional derivative. The operator in the fractional evolution equation is…
In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with time-irregular coefficients. In the finite-dimensional case, we…
We describe an algorithm, based on Euler's method, for solving Volterra integro-differential equations. The algorithm approximates the relevant integral by means of the composite Trapezium Rule, using the discrete nodes of the independent…
The convolution quadrature theory is a systematic approach to analyse the approximation of the Riemann-Liouville fractional operator $I^{\alpha}$ at node $x_{n}$. In this paper, we develop the shifted convolution quadrature ($SCQ$) theory…
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…
Accurate evaluation of nearly singular integrals plays an important role in many boundary integral equation based numerical methods. In this paper, we propose a variant of singularity swapping method to accurately evaluate the layer…
Time dependent quantum systems have become indispensable in science and its applications, particularly at the atomic and molecular levels. Here, we discuss the approximation of closed time dependent quantum systems on bounded domains, via…
This paper deals with the error analysis of the trapezoidal rule for the computation of Fourier type integrals, based on two double exponential transformations. The theory allows to construct algorithms in which the steplength and the…
Recently, general fractional calculus was introduced by Kochubei (2011) and Luchko (2021) as a further generalisation of fractional calculus, where the derivative and integral operator admits arbitrary kernel. Such a formalism will have…
This work proposes algorithms for computing additive and multiplicative free convolutions of two given measures. We consider measures with compact support whose free convolution results in a measure with a density function that exhibits a…
In 1986, Dixon and McKee developed a discrete fractional Gr\"{o}nwall inequality [Z. Angew. Math. Mech., 66 (1986), pp. 535--544], which can be seen as a generalization of the classical discrete Gr\"{o}nwall inequality. However, this…