{"title":"解决带比例卡普托导数的分数常微分方程的新型数值方法","authors":"Yogita M Mahatekar and Pushpendra Kumar","doi":"10.1088/1402-4896/ad7897","DOIUrl":null,"url":null,"abstract":"In this paper, we develop a novel numerical scheme, namely ‘NPCM-PCDE,’ to integrate fractional ordinary differential equations with proportional Caputo derivatives of the type pcDαu(t) = f1(t, u(t)), t ≥ 0, 0 < α < 1 involving a non-linear operator f1. A new method is developed using a natural discretization of the proportional Caputo derivative and the decomposition method to decompose the non-linear operator f1. The error and stability analyses for the proposed method are provided. Some illustrated examples are given to compare the solution curves graphically with the exact solution and to prove the utility and efficiency of the method. The proposed NPCM-PCDE is found to be efficient, easy to implement, convergent, and stable.","PeriodicalId":20067,"journal":{"name":"Physica Scripta","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A novel numerical method to solve fractional ordinary differential equations with proportional Caputo derivatives\",\"authors\":\"Yogita M Mahatekar and Pushpendra Kumar\",\"doi\":\"10.1088/1402-4896/ad7897\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we develop a novel numerical scheme, namely ‘NPCM-PCDE,’ to integrate fractional ordinary differential equations with proportional Caputo derivatives of the type pcDαu(t) = f1(t, u(t)), t ≥ 0, 0 < α < 1 involving a non-linear operator f1. A new method is developed using a natural discretization of the proportional Caputo derivative and the decomposition method to decompose the non-linear operator f1. The error and stability analyses for the proposed method are provided. Some illustrated examples are given to compare the solution curves graphically with the exact solution and to prove the utility and efficiency of the method. The proposed NPCM-PCDE is found to be efficient, easy to implement, convergent, and stable.\",\"PeriodicalId\":20067,\"journal\":{\"name\":\"Physica Scripta\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physica Scripta\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1402-4896/ad7897\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica Scripta","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1402-4896/ad7897","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
A novel numerical method to solve fractional ordinary differential equations with proportional Caputo derivatives
In this paper, we develop a novel numerical scheme, namely ‘NPCM-PCDE,’ to integrate fractional ordinary differential equations with proportional Caputo derivatives of the type pcDαu(t) = f1(t, u(t)), t ≥ 0, 0 < α < 1 involving a non-linear operator f1. A new method is developed using a natural discretization of the proportional Caputo derivative and the decomposition method to decompose the non-linear operator f1. The error and stability analyses for the proposed method are provided. Some illustrated examples are given to compare the solution curves graphically with the exact solution and to prove the utility and efficiency of the method. The proposed NPCM-PCDE is found to be efficient, easy to implement, convergent, and stable.
期刊介绍:
Physica Scripta is an international journal for original research in any branch of experimental and theoretical physics. Articles will be considered in any of the following topics, and interdisciplinary topics involving physics are also welcomed:
-Atomic, molecular and optical physics-
Plasma physics-
Condensed matter physics-
Mathematical physics-
Astrophysics-
High energy physics-
Nuclear physics-
Nonlinear physics.
The journal aims to increase the visibility and accessibility of research to the wider physical sciences community. Articles on topics of broad interest are encouraged and submissions in more specialist fields should endeavour to include reference to the wider context of their research in the introduction.