{"title":"波方程的差分方案","authors":"A. F. Mastryukov","doi":"10.1134/s1995423924010063","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper deals with a numerical solution of a wave equation. The solution algorithm uses optimal parameters which are obtained by using Laguerre transform in time for the wave equation. Additional parameters are introduced into a difference scheme of 2nd-order approximation for the equation. The optimal values of these parameters are obtained by minimizing the error of a difference approximation of the Helmholtz equation. Applying the inverse Laguerre transform in the equation for harmonics, a differential-difference wave equation with the optimal parameters is obtained. This equation is difference in the spatial variables and differential in time. An iterative algorithm for solving the differential-difference wave equation with the optimal parameters is proposed. The results of numerical calculations of the differential-difference equations for 2-dimensional and 1-dimensional versions of the equation are presented. It is shown that the difference schemes with the optimal parameters give an increase in the accuracy of solving the equations.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"8 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Difference Scheme for Wave Equation\",\"authors\":\"A. F. Mastryukov\",\"doi\":\"10.1134/s1995423924010063\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>The paper deals with a numerical solution of a wave equation. The solution algorithm uses optimal parameters which are obtained by using Laguerre transform in time for the wave equation. Additional parameters are introduced into a difference scheme of 2nd-order approximation for the equation. The optimal values of these parameters are obtained by minimizing the error of a difference approximation of the Helmholtz equation. Applying the inverse Laguerre transform in the equation for harmonics, a differential-difference wave equation with the optimal parameters is obtained. This equation is difference in the spatial variables and differential in time. An iterative algorithm for solving the differential-difference wave equation with the optimal parameters is proposed. The results of numerical calculations of the differential-difference equations for 2-dimensional and 1-dimensional versions of the equation are presented. It is shown that the difference schemes with the optimal parameters give an increase in the accuracy of solving the equations.</p>\",\"PeriodicalId\":43697,\"journal\":{\"name\":\"Numerical Analysis and Applications\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-03-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Numerical Analysis and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995423924010063\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995423924010063","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The paper deals with a numerical solution of a wave equation. The solution algorithm uses optimal parameters which are obtained by using Laguerre transform in time for the wave equation. Additional parameters are introduced into a difference scheme of 2nd-order approximation for the equation. The optimal values of these parameters are obtained by minimizing the error of a difference approximation of the Helmholtz equation. Applying the inverse Laguerre transform in the equation for harmonics, a differential-difference wave equation with the optimal parameters is obtained. This equation is difference in the spatial variables and differential in time. An iterative algorithm for solving the differential-difference wave equation with the optimal parameters is proposed. The results of numerical calculations of the differential-difference equations for 2-dimensional and 1-dimensional versions of the equation are presented. It is shown that the difference schemes with the optimal parameters give an increase in the accuracy of solving the equations.
期刊介绍：
Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998.
The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields.
The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.
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