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A multistep collocation method for solving advection equations with delay |
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| Authors: | Bahareh Sadeghi Mohammad Maleki Zeinab Kamali Homa Almasieh |
| Affiliation: | 1. Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran Contribution: Formal analysis, Investigation, Methodology, Software, Writing - original draft, Writing - review & editing;2. Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran;3. Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran Contribution: Formal analysis, Investigation, Supervision, Writing - original draft;4. Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran Contribution: Formal analysis, Investigation, Software, Supervision, Writing - original draft |
| Abstract: | Advection equations with delay are appeared in the modeling of the dynamics of structured cell populations. In this article, we construct an efficient two-dimensional multistep collocation method for the numerical solution of a class of advection equations with delay. Equations with aftereffect and equations with both aftereffect and retardation of a state variable are considered. Computability of the algorithm and convergence properties of the proposed numerical method are analyzed for solutions in appropriate Sobolev spaces, and it is shown that the proposed scheme enjoys the spectral accuracy. Numerical examples are given and comparison with other existing methods in the literature is made to demonstrate the efficiency, superiority and high accuracy of the presented method. |
| Keywords: | advection equation convergence analysis delay partial differential equations Legendre interpolation Legendre–Gauss–Radau collocation |