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Convolution Quadrature
In this chapter, we aim to develop and analyze a class of time-step** schemes for approximately solving the subdiffusion problem (...
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A convolution quadrature using derivatives and its application
This paper is devoted to explore the convolution quadrature based on a class of two-point Hermite collocation methods. Incorporating derivatives into...
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Theta-type convolution quadrature OSC method for nonlocal evolution equations arising in heat conduction with memory
In this paper, we propose a robust and simple technique with efficient algorithmic implementation for numerically solving the nonlocal evolution...
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Convolution Quadrature for Hyperbolic Symbols
In this chapter we introduce the operational calculus that forms the basis of the analysis of the problems this book investigates, i.e., we give a...
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The Unified Theory of Shifted Convolution Quadrature for Fractional Calculus
This work devotes to develo** a systematic and convenient approach based on the celebrated convolution quadrature theory to design and analyze...
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An Optimal Quadrature Formula for Numerical Integration of the Right Riemann–Liouville Fractional Integral
AbstractIn the present article, the problem of construction of the optimal quadrature formula for numerical integration of the right...
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Numerical schemes for the time-fractional mobile/immobile transport equation based on convolution quadrature
In this work, the numerical approximation of the time-fractional mobile/immobile transport equation is considered. We investigate the solution...
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The discrete analogue of high-order differential operator and its application to finding coefficients of optimal quadrature formulas
The discrete analog of the differential operator plays a significant role in constructing interpolation, quadrature, and cubature formulas. In this...
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Double exponential quadrature for fractional diffusion
We introduce a novel discretization technique for both elliptic and parabolic fractional diffusion problems based on double exponential quadrature...
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A Numerical Study of the Convergence of Two Hybrid Convolution Quadrature Schemes for Broadband Wave Problems
In this chapter, we compare the performance of two recently proposed hybrid methods for numerically solving the wave equation in two spatial...
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A Convolution Quadrature Method for Maxwell’s Equations in Dispersive Media
We study the systematic numerical approximation of Maxwell’s equations in dispersive media. Two discretization strategies are considered, one based...
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Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators
The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-step** schemes...
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Construction of an Optimal Quadrature Formula in the Hilbert Space of Periodic Functions
AbstractThis paper is devoted to constructing a new optimal quadrature formula in the Gilbert space of real-valued, periodic functions. Here, the...
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On superconvergence of Runge–Kutta convolution quadrature for the wave equation
The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral...
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A Single-Step Correction Scheme of Crank–Nicolson Convolution Quadrature for the Subdiffusion Equation
We develop a new correction scheme for time discretization of the subdiffusion equation based on the fractional Crank–Nicolson convolution...
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Quadrature Domains for the Helmholtz Equation with Applications to Non-scattering Phenomena
In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called...
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Transparent boundary conditions for wave propagation in fractal trees: convolution quadrature approach
In this work we propose high-order transparent boundary conditions for the weighted wave equation on a fractal tree, with an application to the...
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An overview on a time discrete convolution—space collocation BEM for 2D exterior wave propagation problems
We consider 2D transient linear wave propagation problems defined in the exterior of bounded domains. In particular, we first consider the problem...
