 A spectral method for dispersive solutions of the nonlocal Sine–Gordon equationA. Coclite, L. Lopez and S.F. Pellegrino Mathematics and Computers in Simulation (MATCOM), 2025, vol. 234, issue C, 235-247 Abstract: Moved by the need for rigorous and reliable numerical tools for the analysis of peridynamic materials, the authors propose a model able to capture the dispersive features of nonlocal soliton-like solutions obtained by a peridynamic formulation of the Sine–Gordon equation. The analysis of the Cauchy problem associated to the peridynamic Sine–Gordon equation with local Neumann boundary condition is performed in this work through a spectral method on Chebyshev polynomials nodes joined with the Störmer–Verlet scheme for the time evolution. The choice for using the spectral method resides in the resulting reachable numerical accuracy, while, indeed, Chebyshev polynomials allow straightforward implementation of local boundary conditions. Several numerical experiments are proposed for thoroughly describe the ability of such scheme. Specifically, dispersive effects of the specific peridynamic kernel are demonstrated, while the internal energy behavior of the specified peridynamic operator is studied. Keywords: Peridynamics; Nonlocal Sine–Gordon; Spectral methods; Nonlocal solitons; Numerical methods (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:234:y:2025:i:c:p:235-247 DOI: 10.1016/j.matcom.2025.02.028 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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