| Autor: |
Jorge E. Macías-Díaz, Tassos Bountis |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Fractal and Fractional, Vol 6, Iss 9, p 500 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2504-3110 |
| DOI: |
10.3390/fractalfract6090500 |
| Popis: |
For the first time, a new dissipation-preserving scheme is proposed and analyzed to solve a Caputo–Riesz time-space-fractional multidimensional nonlinear wave equation with generalized potential. We consider initial conditions and impose homogeneous Dirichlet data on the boundary of a bounded hyper cube. We introduce an energy-type functional and prove that the new mathematical model obeys a conservation law. Motivated by these facts, we propose a finite-difference scheme to approximate the solutions of the continuous model. A discrete form of the continuous energy is proposed and the discrete operator is shown to satisfy a conservation law, in agreement with its continuous counterpart. We employ a fixed-point theorem to establish theoretically the existence of solutions and study analytically the numerical properties of consistency, stability and convergence. We carry out a number of numerical simulations to verify the validity of our theoretical results. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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