Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation
سال انتشار: 1394
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 232
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شناسه ملی سند علمی:
JR_CMDE-3-3_001
تاریخ نمایه سازی: 15 اسفند 1401
چکیده مقاله:
In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of derivatives. All principles and properties of the ESC functions are derived and introduced by us as a new basis defined in the whole range. The method transforms the PDEs and conditions into block matrix equations, which correspond to system of linear algebraic equations with unknown ESC coefficients, by using ESC collocation points. Combining these matrix equations and then solving the system yield the ESC coefficients of the solution function. Numerical examples are included to test the validity and applicability of the method.
کلیدواژه ها:
Exponential second kind Chebyshev functions ، High-order partial differential equations ، Collocation method
نویسندگان
Mohamed Abdel-Latif Ramadan
Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt
Kamal Mohamed Raslsn
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
Talaat El-Sayed El-Danaf
Department of Mathematics and Statistics, Taibah University Madinah Munawwarah, KSA
Mohamed Abd El Salam
Mathematics Department, Faculty of Science Al-Azhar University, Nasr-City, ۱۱۸۸۴, Cairo, Egypt