Efficient exponential Rosenbrock methods till order four

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-07-23 DOI:10.1016/j.cam.2024.116158

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引用次数: 0

Abstract

In a previous paper, a technique was described to avoid order reduction with exponential Rosenbrock methods when integrating initial boundary value problems with time-dependent boundary conditions. That requires to calculate some information on the boundary from the given data. In the present paper we prove that, under some assumptions on the coefficients of the method which are mainly always satisfied, no numerical differentiation is required to approximate that information in order to achieve order 4 for parabolic problems with Dirichlet boundary conditions. With Robin/Neumann ones, just numerical differentiation in time may be necessary for order 4, but none for order $\leq 3$ .

Furthermore, as with this technique it is not necessary to impose any stiff order conditions, in search of efficiency, we recommend some methods of classical orders 2, 3 and 4 and we give some comparisons with several methods in the literature, with the corresponding stiff order.

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直到四阶的高效指数罗森布洛克方法

在之前的一篇论文中，介绍了一种在积分具有时间相关边界条件的初始边界值问题时，避免指数罗森布洛克方法阶次降低的技术。这需要从给定数据中计算出一些边界信息。在本文中，我们证明了在方法系数的一些假设条件下（这些假设条件主要是始终满足的），不需要数值微分来近似这些信息，就能使具有 Dirichlet 边界条件的抛物线问题达到 4 阶。对于 Robin/Neumann 方法，阶数 4 可能只需要时间数值微分，而阶数 ≤3 则不需要。此外，由于该技术不需要施加任何硬阶数条件，为了提高效率，我们推荐了一些经典的阶数为 2、3 和 4 的方法，并与文献中几种具有相应硬阶数的方法进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.