{"title":"解决时空分数阶波方程的保角映射和切比雪夫配位法混合技术","authors":"Adel Abd Elaziz El-Sayed, Salah Boulaaras","doi":"10.1002/jnm.3220","DOIUrl":null,"url":null,"abstract":"<p>This work presents a numerical approach for solving the time–space fractional-order wave equation. The time-fractional derivative is described in the conformal sense, whereas the space-fractional derivative is given in the Caputo sense. The investigated technique is based on the third-kind of shifted Chebyshev polynomials. The main problem is converted into a system of ordinary differential equations using conformal mapping, Caputo derivatives, and the properties of the third-kind shifted Chebyshev polynomials. Then, the Chebyshev collocation method and the non-standard finite difference method will be used to convert this system into a system of algebraic equations. Finally, this system can be solved numerically via Newton's iteration method. In the end, physics numerical examples and comparison results are provided to confirm the accuracy, applicability, and efficiency of the suggested approach.</p>","PeriodicalId":50300,"journal":{"name":"International Journal of Numerical Modelling-Electronic Networks Devices and Fields","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hybrid technique of conformal mapping and Chebyshev collocation method for solving time–space fractional order wave equation\",\"authors\":\"Adel Abd Elaziz El-Sayed, Salah Boulaaras\",\"doi\":\"10.1002/jnm.3220\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This work presents a numerical approach for solving the time–space fractional-order wave equation. The time-fractional derivative is described in the conformal sense, whereas the space-fractional derivative is given in the Caputo sense. The investigated technique is based on the third-kind of shifted Chebyshev polynomials. The main problem is converted into a system of ordinary differential equations using conformal mapping, Caputo derivatives, and the properties of the third-kind shifted Chebyshev polynomials. Then, the Chebyshev collocation method and the non-standard finite difference method will be used to convert this system into a system of algebraic equations. Finally, this system can be solved numerically via Newton's iteration method. In the end, physics numerical examples and comparison results are provided to confirm the accuracy, applicability, and efficiency of the suggested approach.</p>\",\"PeriodicalId\":50300,\"journal\":{\"name\":\"International Journal of Numerical Modelling-Electronic Networks Devices and Fields\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-02-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Numerical Modelling-Electronic Networks Devices and Fields\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/jnm.3220\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Numerical Modelling-Electronic Networks Devices and Fields","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jnm.3220","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Hybrid technique of conformal mapping and Chebyshev collocation method for solving time–space fractional order wave equation
This work presents a numerical approach for solving the time–space fractional-order wave equation. The time-fractional derivative is described in the conformal sense, whereas the space-fractional derivative is given in the Caputo sense. The investigated technique is based on the third-kind of shifted Chebyshev polynomials. The main problem is converted into a system of ordinary differential equations using conformal mapping, Caputo derivatives, and the properties of the third-kind shifted Chebyshev polynomials. Then, the Chebyshev collocation method and the non-standard finite difference method will be used to convert this system into a system of algebraic equations. Finally, this system can be solved numerically via Newton's iteration method. In the end, physics numerical examples and comparison results are provided to confirm the accuracy, applicability, and efficiency of the suggested approach.
期刊介绍:
Prediction through modelling forms the basis of engineering design. The computational power at the fingertips of the professional engineer is increasing enormously and techniques for computer simulation are changing rapidly. Engineers need models which relate to their design area and which are adaptable to new design concepts. They also need efficient and friendly ways of presenting, viewing and transmitting the data associated with their models.
The International Journal of Numerical Modelling: Electronic Networks, Devices and Fields provides a communication vehicle for numerical modelling methods and data preparation methods associated with electrical and electronic circuits and fields. It concentrates on numerical modelling rather than abstract numerical mathematics.
Contributions on numerical modelling will cover the entire subject of electrical and electronic engineering. They will range from electrical distribution networks to integrated circuits on VLSI design, and from static electric and magnetic fields through microwaves to optical design. They will also include the use of electrical networks as a modelling medium.