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Pré-Publication, Document De Travail Année : 2022

Compact schemes in time with applications to partial differential equations

Stéphane Clain
Gaspar Machado
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  • PersonId : 911820
Maria Teresa Malheiro
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  • PersonId : 1174501

Résumé

We propose a new class of fourth-and sixth-order schemes in time for parabolic and hyperbolic equations. The method follows the compact scheme methodology by elaborating implicit relations between the approximations of the function and its derivatives. We produce a series of A-stable methods with low dispersion and high accuracy. Several benchmarks for linear and non-linear Ordinary Differential Equations demonstrate the effectiveness of the method. Then a second set of numerical benchmarks for Partial Differential Equations such as convectiondiffusion, Schrödinger equation, wave equation, Bürgers, and Euler system give the numerical evidences of the superior advantage of the method with respect to the traditional Runge-Kutta or multistep methods.
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Dates et versions

hal-03814183 , version 1 (13-10-2022)

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  • HAL Id : hal-03814183 , version 1

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Stéphane Clain, Gaspar Machado, Maria Teresa Malheiro. Compact schemes in time with applications to partial differential equations. 2022. ⟨hal-03814183⟩

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