Journal
FRACTAL AND FRACTIONAL
Volume 6, Issue 4, Pages -Publisher
MDPI
DOI: 10.3390/fractalfract6040201
Keywords
nonlinear fourth-order fractional integro-differential equation; WSGI approximation; BDF2; mixed finite element method
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Funding
- Natural Science Foundation of Inner Mongolia [2020MS01003, 2021MS01018]
- Young Innovative Talents Project of Grassland Talents Project
- Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region [NMGIRT2207]
- National Innovation Project [202010126022]
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This article studies a class of nonlinear fourth-order partial differential equation models with the Riemann-Liouville fractional integral term in two dimensions. The mixed element method is used in space, while the second-order backward difference formula (BDF2) with the weighted and shifted Grunwald integral (WSGI) formula is used in time. Stability and error results for the fully discrete scheme are derived, and two numerical examples are provided to verify the theoretical results.
In this article, we study a class of two-dimensional nonlinear fourth-order partial differential equation models with the Riemann-Liouville fractional integral term by using a mixed element method in space and the second-order backward difference formula (BDF2) with the weighted and shifted Grunwald integral (WSGI) formula in time. We introduce an auxiliary variable to transform the nonlinear fourth-order model into a low-order coupled system including two second-order equations and then discretize the resulting equations by the combined method between the BDF2 with the WSGI formula and the mixed finite element method. Further, we derive stability and error results for the fully discrete scheme. Finally, we develop two numerical examples to verify the theoretical results.
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