{"title":"A High-Precision Meshless Method for Time-Fractional Mixed Diffusion and Wave Equations","authors":"Zehui Ma, Rahmatjan Imin","doi":"10.1002/nme.70020","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this paper, a meshless scheme based on Kernel Derivative Free Smoothed Particle Hydrodynamics (KDF-SPH) approximation is proposed to solve the time-fractional mixed diffusion and wave equations. The time fractional derivative is defined in the Caputo sense, and we use the finite difference method to discretize. The meshless method based on KDF-SPH is used for spatial discretization. Thus, a fully discrete meshless numerical scheme is obtained. At the same time, we use the obtained meshless discrete scheme to solve the initial boundary value problems of time-fractional mixed diffusion and wave equations in regular and irregular regions, and we get good results. By comparing the proposed method with many numerical methods, the accuracy and effectiveness of the proposed method are further verified.</p>\n </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 6","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nme.70020","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, a meshless scheme based on Kernel Derivative Free Smoothed Particle Hydrodynamics (KDF-SPH) approximation is proposed to solve the time-fractional mixed diffusion and wave equations. The time fractional derivative is defined in the Caputo sense, and we use the finite difference method to discretize. The meshless method based on KDF-SPH is used for spatial discretization. Thus, a fully discrete meshless numerical scheme is obtained. At the same time, we use the obtained meshless discrete scheme to solve the initial boundary value problems of time-fractional mixed diffusion and wave equations in regular and irregular regions, and we get good results. By comparing the proposed method with many numerical methods, the accuracy and effectiveness of the proposed method are further verified.
期刊介绍：
The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems.
The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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