A modified Gautschi’s method without order reduction when integrating boundary value nonlinear wave problems

B. Cano and M.J. Moreta

Applied Mathematics and Computation, 2020, vol. 373, issue C

Abstract: In this paper we analyse the order reduction which turns up when integrating nonlinear wave problems with non-homogeneous and time-dependent boundary conditions with the well-known Gautschi’s method. Moreover, a technique is suggested to avoid that order reduction so that the classical local order 4 and global order 2 are recovered. On the other hand, the usual approximation for the derivative which is used together with this method is also analysed and a substantial improvement is suggested. Some numerical results are shown which corroborate the performed analysis.

Keywords: Gautschi’s method; Initial boundary value problem; Nonlinear wave equations; Avoiding order reduction (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:373:y:2020:i:c:s0096300319310148

DOI: 10.1016/j.amc.2019.125022

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