Sixth-order Finite Difference Schemes for Nonlinear Wave Equations with Variable Coefficients in Three Dimensions

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

International Journal of Computer Mathematics Pub Date : 2023-11-01 DOI:10.1080/00207160.2023.2279006

Shuaikang Wang, Yongbin Ge, Tingfu Ma

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引用次数: 0

Abstract

AbstractFirst, a nonlinear difference scheme is proposed to solve the three-dimensional (3D) nonlinear wave equation by combining the correction technique of truncation error remainder in time and a sixth-order finite difference operator in space, resulting in fourth-order accuracy in time and sixth-order accuracy in space. Then, the Richardson extrapolation method is applied to improve the temporal accuracy from the fourth-order to the sixth-order. To enhance computational efficiency, a linearized difference scheme is obtained by linear interpolation based on the nonlinear scheme. In addition, the stability of the linearized scheme is proved. Finally, the accuracy, stability and efficiency of the two proposed schemes are tested numerically.Keywords: Three-dimensional nonlinear wave equationNonlinear difference schemeSixth-order accuracyLinearized difference schemeRichardson extrapolationDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis work is partially supported by National Natural Science Foundation of China (12161067), Natural Science Foundation of Ningxia (2022AAC02023, 2022AAC03313), the Key Research and Development Program of Ningxia (2021YCZX0036, 2021BEB04053), the Scientific Research Program in Higher Institution of Ningxia (NGY2020110), National Youth Top-notch Talent Support Program of Ningxia.Data AvailabilityThe data used to support the findings of this study are available from the corresponding author upon request. Conflicts of InterestThe authors declare no conflict of interest.

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三维变系数非线性波动方程的六阶有限差分格式

摘要首先，将截断误差余数在时间上的校正技术与空间上的六阶有限差分算子相结合，提出了求解三维非线性波动方程的非线性差分格式，得到了时间上的四阶精度和空间上的六阶精度。然后，采用Richardson外推法将时间精度从四阶提高到六阶。为了提高计算效率，在非线性格式的基础上，通过线性插值得到线性化差分格式。此外，还证明了线性化方案的稳定性。最后，对两种方案的精度、稳定性和效率进行了数值验证。关键词:三维非线性波动方程非线性差分格式六阶精度线性化差分格式richardson外推免责声明作为对作者和研究人员的服务，我们提供此版本的已接受稿件(AM)。在最终出版版本记录(VoR)之前，将对该手稿进行编辑、排版和审查。在制作和印前，可能会发现可能影响内容的错误，所有适用于期刊的法律免责声明也与这些版本有关。国家自然科学基金项目(12161067)、宁夏自然科学基金项目(2022AAC02023、2022AAC03313)、宁夏重点研发计划项目(2021YCZX0036、2021BEB04053)、宁夏高校科研计划项目(NGY2020110)、宁夏国家青年拔尖人才支持计划项目资助。数据可获得性用于支持本研究结果的数据可应要求从通讯作者处获得。利益冲突作者声明无利益冲突。

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来源期刊

International Journal of Computer Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

5 months

期刊介绍： International Journal of Computer Mathematics (IJCM) is a world-leading journal serving the community of researchers in numerical analysis and scientific computing from academia to industry. IJCM publishes original research papers of high scientific value in fields of computational mathematics with profound applications to science and engineering. IJCM welcomes papers on the analysis and applications of innovative computational strategies as well as those with rigorous explorations of cutting-edge techniques and concerns in computational mathematics. Topics IJCM considers include: • Numerical solutions of systems of partial differential equations • Numerical solution of systems or of multi-dimensional partial differential equations • Theory and computations of nonlocal modelling and fractional partial differential equations • Novel multi-scale modelling and computational strategies • Parallel computations • Numerical optimization and controls • Imaging algorithms and vision configurations • Computational stochastic processes and inverse problems • Stochastic partial differential equations, Monte Carlo simulations and uncertainty quantification • Computational finance and applications • Highly vibrant and robust algorithms, and applications in modern industries, including but not limited to multi-physics, economics and biomedicine. Papers discussing only variations or combinations of existing methods without significant new computational properties or analysis are not of interest to IJCM. Please note that research in the development of computer systems and theory of computing are not suitable for submission to IJCM. Please instead consider International Journal of Computer Mathematics: Computer Systems Theory (IJCM: CST) for your manuscript. Please note that any papers submitted relating to these fields will be transferred to IJCM:CST. Please ensure you submit your paper to the correct journal to save time reviewing and processing your work. Papers developed from Conference Proceedings Please note that papers developed from conference proceedings or previously published work must contain at least 40% new material and significantly extend or improve upon earlier research in order to be considered for IJCM.