University of Tabriz Computational Methods for Differential Equations 2345-3982 3 3 2015 07 01 Solving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation 147 162 4716 EN 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, 11884, Cairo, Egypt Journal Article 2015 12 30 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. https://cmde.tabrizu.ac.ir/article_4716_865a972e969ce0256b6db9b8006f6073.pdf