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Exponential quadrature rules without order reduction for integrating linear initial boundary value problems

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Cano Urdiales, Begoña and Moreta Santos, María Jesús (2018) Exponential quadrature rules without order reduction for integrating linear initial boundary value problems. SIAM Journal on Numerical Analysis, 56 (3). pp. 1187-1209. ISSN 0036-1429

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Official URL: https://doi.org/10.1137/17M1124279



Abstract

In this paper a technique is suggested to integrate linear initial boundary value problems with exponential quadrature rules in such a way that the order in time is as high as possible. A thorough error analysis is given both for the classical approach of integrating the problem first in space and then in time and for doing it in the reverse order in a suitable manner. Time-dependent boundary conditions are considered with both approaches and full discretization formulas are given to implement the methods once the quadrature nodes have been chosen for the time integration and a particular (although very general) scheme is selected for the space discretization. Numerical experiments are shown which corroborate that, for example with the suggested technique, order 2s is obtained when choosing the s nodes of the Gaussian quadrature rule.


Item Type:Article
Uncontrolled Keywords:Exponential quadrature rules; Linear initial boundary value problems; Avoiding order reduction
Subjects:Sciences > Mathematics
ID Code:60775
Deposited On:04 Jun 2020 10:24
Last Modified:05 Jun 2020 08:28

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