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

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.