Convolution Quadrature Revisited

By Christian Lubich. 2004

183 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mechanics of Materials, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b76d70f592a783aa633a5c9aad2d31eb907cf74d

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In Applied Mathematics

In Mechanics of Materials

In Numerical Analysis

Citations in the corpus

An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data (2017, methodology): “Based on Lubich’s convolution quadrature [30], [31], [32], the Riemann-Liouville fractional derivative 0D α t u(t) can be approximated by, with 0 < α < 1,”
An error analysis of Runge–Kutta convolution quadrature (2011, methodology): “Convolution quadrature methods based on numerical methods for ordinary differential equations, such as multistep or Runge-Kutta methods, have proved very effective: they offer built-in stability, they require only knowledge of the Laplace transformK(s) of the convolution kernel k(t) rather than the ”
The Exponentially Convergent Trapezoidal Rule (2014, methodology): “Another variation on the theme is the use of the method known as convolution quadrature [106].”
Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview (2018, methodology): “Convolution quadrature (CQ) was first proposed by Lubich in a series of works [66, 67, 68] for discretizing Volterra integral equations.”
Numerical analysis for distributed-order differential equations (2009, methodology): “Step 2 finally will consist of solving the system we have constructed numerically by any of the available methods; one could for example use the Adams method of [16] or the backward differentiation scheme of [9] or a fractional multistep method (see [20, 21, 22, 14]) which is likely to be efficient ”
Convolution quadrature time discretization of fractional diffusion-wave equations (2006, methodology): “A convolution quadrature [21, 22 ] approximates the continuous convolution”
Generalized convolution quadrature with variable time stepping (2013, methodology): “For this type of problems, the convolution quadrature method has been developed originally by Lubich, see [6, 7, 10, 9] for parabolic problems and [8] for hyperbolic ones.”
Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial (2018, methodology): “When f (t) is sufficiently smooth and the LMM has order p of convergence, the approximation provided by Equation (17) satisfies [33] (Theorem 2.”
Runge-Kutta convolution quadrature for the Boundary Element Method (2012, background): “Beside these improved approaches there exists the possibility to solve the convolution integral in the boundary integral equation with the so-called Convolution Quadrature Method (CQM) proposed by Lubich[10,11].”
A practical guide to Prabhakar fractional calculus (2020, background): “Its generalization to β > 0 is however immediate and is achieved by following the same steps illustrated in [36] and by taking profit of Lubich’s theory [92–94] of generalized convolution quadratures.”