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.