A new numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ equation-Reference-Cited by-同舟云学术

A new numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ equation

Published:2022-10-04 Issue:0 Volume:0 Page:
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Chawla Reetika¹,Deswal Komal¹,Kumar Devendra¹^ORCID

Affiliation:

1. Department of Mathematics , Birla Institute of Technology and Science , Pilani , Rajasthan 333031 , India

Abstract

Abstract In this article, we present a novel numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ (BBMB) equation using Atangana Baleanu Caputo (ABC) derivative. First, we apply a linearization technique to deal with the generalized non-linear expression, and then the Crank–Nicolson finite difference formula is used in the temporal direction. A reliable numerical technique is applied to discretize the time-fractional ABC derivative, and the central difference formulae are used to approximate the derivatives in the spatial direction. The method is shown unconditionally stable and second-order convergent in both directions through the Fourier analysis. The numerical results of two test problems are analyzed to validate the theoretical results.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2022-0209/pdf

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