Highly Efficient Method for Solving Parabolic PDE with Nonlocal Boundary Conditions - Applied Mathematics

AM > Vol.13 No.2, February 2022

Applied Mathematics

Volume 13, Issue 2 (February 2022)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

Highly Efficient Method for Solving Parabolic PDE with Nonlocal Boundary Conditions ()

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DOI: 10.4236/am.2022.132009 196 Downloads 1,196 Views Citations

Author(s)

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

Affiliation(s)

Department of Mathematical Sciences, Faculty of Engineering, Mansoura University, Egypt.

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.

KEYWORDS

Chelyshkov, Collocation Method, Parabolic, Nonlocal Boundary Conditions

Share and Cite:

El-Gamel, M. , El-Baghdady, G. and El-Hady, M. (2022) Highly Efficient Method for Solving Parabolic PDE with Nonlocal Boundary Conditions. Applied Mathematics, 13, 101-119. doi: 10.4236/am.2022.132009.

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