A predictor–corrector compact finite difference scheme for a nonlinear partial integro-differential equation
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Shufang Hu
,
Wenlin Qiu
Abstract
A predictor–corrector compact finite difference scheme is proposed for a nonlinear partial integro-differential equation. In our method, the time direction is approximated by backward Euler scheme and the Riemann–Liouville (R–L) fractional integral term is treated by means of first order convolution quadrature suggested by Lubich. Meanwhile, a two-step predictor–corrector (P–C) algorithm called MacCormack method is used. A fully discrete scheme is constructed with space discretization by compact finite difference method. Numerical experiment presents the scheme is in good agreement with the theoretical analysis.
Funding source: The Scientific Reasearch Foundation of Hunan Provincial Education Department doi.org/10.13039/100014472
Award Identifier / Grant number: 17B277
Award Identifier / Grant number: 18C0137
Funding source: The Startup Scientific Research Foundation of CSUFT
Award Identifier / Grant number: 2017YJ026
Funding source: The project supported by the Natural Science Foundation of Hunan Province
Award Identifier / Grant number: 2018JJ2669
Acknowledgement
We thank anonymous referees for their careful review on our manuscript and for their constructive comments.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: The project supported by the Natural Science Foundation of Hunan Province (No: 2018JJ2669), the Scientific Research Foundation of Hunan Provincial Education Department (No: 17B277, 18C0137) and the Startup Scientific Research Foundation of CSUFT (No: 2017YJ026).
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Dynamics of synthetic drug transmission models
- Collision-induced amplitude dynamics of pulses in linear waveguides with the generic nonlinear loss
- Global dissipativity of non-autonomous BAM neural networks with mixed time-varying delays and discontinuous activations
- On the inverse problem for nonlinear strongly damped wave equations with discrete random noise
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- Propagation of diffusing pollutant by kinetic flux-vector splitting method
- Limit cycles in a tritrophic food chain model with general functional responses
- Local and parallel stabilized finite element methods based on full domain decomposition for the stationary Stokes equations
- Stress concentration effect on deflection and stress fields of a master leaf spring through domain decomposition and geometry updation technique
- Electrostatically actuated double walled piezoelectric nanoshell subjected to nonlinear van der Waals effect: nonclassical vibrations and stability analysis
- Traveling wave solutions of the generalized Rosenau–Kawahara-RLW equation via the sine–cosine method and a generalized auxiliary equation method
- A predictor–corrector compact finite difference scheme for a nonlinear partial integro-differential equation
- Parameter inference with analytical propagators for stochastic models of autoregulated gene expression
- DCSK performance analysis of a chaos-based communication using a newly designed chaotic system
- On successive linearization method for differential equations with nonlinear conditions
- Comparison of different time discretization schemes for solving the Allen–Cahn equation
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