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Ramadan, Mohamed Abdel-Latif, Raslsn, Kamal Mohamed, El-Danaf, Talaat El-Sayed, Abd El Salam, Mohamed. (1394). Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation. سامانه مدیریت نشریات علمی, 3(3), 147-162.
Mohamed Abdel-Latif Ramadan; Kamal Mohamed Raslsn; Talaat El-Sayed El-Danaf; Mohamed Abd El Salam. "Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation". سامانه مدیریت نشریات علمی, 3, 3, 1394, 147-162.
Ramadan, Mohamed Abdel-Latif, Raslsn, Kamal Mohamed, El-Danaf, Talaat El-Sayed, Abd El Salam, Mohamed. (1394). 'Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation', سامانه مدیریت نشریات علمی, 3(3), pp. 147-162.
Ramadan, Mohamed Abdel-Latif, Raslsn, Kamal Mohamed, El-Danaf, Talaat El-Sayed, Abd El Salam, Mohamed. Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation. سامانه مدیریت نشریات علمی, 1394; 3(3): 147-162.

Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation

Computational Methods for Differential Equations
مقاله 7، دوره 3، شماره 3، مهر 2015، صفحه 147-162    اصل مقاله (1.47 M)
نوع مقاله: Research Paper
نویسندگان
Mohamed Abdel-Latif Ramadan1؛ Kamal Mohamed Raslsn2؛ Talaat El-Sayed El-Danaf3؛ Mohamed Abd El Salam* 4
1Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt
2Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
3Department of Mathematics and Statistics, Taibah University Madinah Munawwarah, KSA
4Mathematics Department, Faculty of Science Al-Azhar University, Nasr-City, 11884, Cairo, Egypt
چکیده
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.
کلیدواژه‌ها
Exponential second kind Chebyshev functions؛ High-order partial differential equations؛ Collocation method
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