{"title":"十四阶边值问题的Haar小波解法","authors":"Rohul Amin, Imran Khan, Şuayip Yüzbaşı","doi":"10.1002/jnm.70104","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>Higher-order boundary value problems (BVP) of differential equations (DEs) are important in the mathematical description of many real-world processes. Solving such problems for exact or analytical solutions is not always easy to deal. Therefore, to compute their numerical solution, we need some numerical methods. Hence, in this work, a powerful numerical procedure based on Haar Wavelet (HW) method is established to deal with fourteenth-order BVPs linear and nonlinear. A generalized form of the algorithm is developed under general boundary conditions. Then the numerical method is verified on various examples from the literature. Also, maximum and root mean square errors are calculated. Moreover, a comparison between exact and numerical results is shown at different collocation points. Furthermore, convergence rate is approximately 2 at various numbers of nodal points is also calculated.</p>\n </div>","PeriodicalId":50300,"journal":{"name":"International Journal of Numerical Modelling-Electronic Networks Devices and Fields","volume":"38 5","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Haar Wavelet Method for the Solution of Fourteenth Order Boundary Value Problems\",\"authors\":\"Rohul Amin, Imran Khan, Şuayip Yüzbaşı\",\"doi\":\"10.1002/jnm.70104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>Higher-order boundary value problems (BVP) of differential equations (DEs) are important in the mathematical description of many real-world processes. Solving such problems for exact or analytical solutions is not always easy to deal. Therefore, to compute their numerical solution, we need some numerical methods. Hence, in this work, a powerful numerical procedure based on Haar Wavelet (HW) method is established to deal with fourteenth-order BVPs linear and nonlinear. A generalized form of the algorithm is developed under general boundary conditions. Then the numerical method is verified on various examples from the literature. Also, maximum and root mean square errors are calculated. Moreover, a comparison between exact and numerical results is shown at different collocation points. Furthermore, convergence rate is approximately 2 at various numbers of nodal points is also calculated.</p>\\n </div>\",\"PeriodicalId\":50300,\"journal\":{\"name\":\"International Journal of Numerical Modelling-Electronic Networks Devices and Fields\",\"volume\":\"38 5\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-09-02\",\"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.70104\",\"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.70104","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}
Haar Wavelet Method for the Solution of Fourteenth Order Boundary Value Problems
Higher-order boundary value problems (BVP) of differential equations (DEs) are important in the mathematical description of many real-world processes. Solving such problems for exact or analytical solutions is not always easy to deal. Therefore, to compute their numerical solution, we need some numerical methods. Hence, in this work, a powerful numerical procedure based on Haar Wavelet (HW) method is established to deal with fourteenth-order BVPs linear and nonlinear. A generalized form of the algorithm is developed under general boundary conditions. Then the numerical method is verified on various examples from the literature. Also, maximum and root mean square errors are calculated. Moreover, a comparison between exact and numerical results is shown at different collocation points. Furthermore, convergence rate is approximately 2 at various numbers of nodal points is also calculated.
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.
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