{"title":"求解分数偏微分方程的空间六阶数值方案","authors":"","doi":"10.1016/j.aml.2024.109265","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, a spatial sixth-order numerical scheme for solving the time-fractional diffusion equation (TFDE) is proposed. The convergence order of the constructed numerical scheme is <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>τ</mi></math></span> and <span><math><mi>h</mi></math></span> are the temporal and spatial step sizes, respectively. The stability and error estimation of proposed scheme are given by using Fourier method. Some numerical examples are studied to demonstrate the correctness and effectiveness of the scheme and validate the theoretical analysis.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A spatial sixth-order numerical scheme for solving fractional partial differential equation\",\"authors\":\"\",\"doi\":\"10.1016/j.aml.2024.109265\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, a spatial sixth-order numerical scheme for solving the time-fractional diffusion equation (TFDE) is proposed. The convergence order of the constructed numerical scheme is <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>6</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>τ</mi></math></span> and <span><math><mi>h</mi></math></span> are the temporal and spatial step sizes, respectively. The stability and error estimation of proposed scheme are given by using Fourier method. Some numerical examples are studied to demonstrate the correctness and effectiveness of the scheme and validate the theoretical analysis.</p></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965924002854\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002854","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
本文提出了一种求解时间分数扩散方程（TFDE）的空间六阶数值方案。所建数值方案的收敛阶数为 O(τ2+h6)，其中 τ 和 h 分别为时间步长和空间步长。利用傅立叶方法给出了拟议方案的稳定性和误差估计。研究了一些数值示例，以证明该方案的正确性和有效性，并验证理论分析。
A spatial sixth-order numerical scheme for solving fractional partial differential equation
In this paper, a spatial sixth-order numerical scheme for solving the time-fractional diffusion equation (TFDE) is proposed. The convergence order of the constructed numerical scheme is , where and are the temporal and spatial step sizes, respectively. The stability and error estimation of proposed scheme are given by using Fourier method. Some numerical examples are studied to demonstrate the correctness and effectiveness of the scheme and validate the theoretical analysis.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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