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Bastani, M. and Salkuyeh, D. (2013) Numerical Studies of a Non-Local Parabolic Partial Differential Equations by Spectral Collocation Method with Preconditioning. Computational Mathematics and Modeling, 24, 81-89.
https://doi.org/10.1007/s10598-013-9161-6

has been cited by the following article:

• TITLE: Highly Efficient Method for Solving Parabolic PDE with Nonlocal Boundary Conditions

  AUTHORS: Mohamed El-Gamel, Galal I. El-Baghdady, Mahmoud Abd El-Hady

  KEYWORDS: Chelyshkov, Collocation Method, Parabolic, Nonlocal Boundary Conditions

  JOURNAL NAME: Applied Mathematics, Vol.13 No.2, February 10, 2022

  ABSTRACT: In this work, a highly efficient algorithm is developed for solving the parabolic partial differential equation (PDE) with the nonlocal condition. For this purpose, we employ orthogonal Chelyshkov polynomials as the basis. The convergence analysis of the proposed scheme is derived. Numerical experiments are carried out to explain the efficiency and precision of the proposed scheme. Furthermore, the reliability of the scheme is verified by comparisons with assured existing methods.