An Improved Numerical Scheme for 2D Nonlinear Time-Dependent Partial Integro-Differential Equations with Multi-Term Fractional Integral Items
Year: 2025
Type: article
Abstract: This paper is dedicated to investigating a highly accurate numerical solution for a class of 2D nonlinear time-dependent partial integro-differential equations with multi-term fractional integral items. These integrals are weakly singular with respect to time, which are handled using the product integration rule on graded meshes to compensate for the influence generated by the initial weak singular nature of the exact solution. The temporal derivative is approximated by a generalized Crank–Nicolson difference scheme, while the nonlinear term is approximated by a linearized method. Furthermore, the stability and convergence of the derived time semi-discretization scheme are strictly proved by revising the finite discrete parameters. Meanwhile, the differential matrices of the spatial high-order derivatives based on barycentric rational interpolation are utilized to obtain the fully discrete scheme. Finally, the effectiveness and reliability of the proposed method are validated by means of several numerical experiments.
Source: Fractal and Fractional
Authors: Fan Ouyang, Hongyan Liu, Yanying Ma
Institutions: Guizhou University, Anhui Jianzhu University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,258
OpenAlex ID: W4408336596