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GaraiEtAl2026c
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<span id="GaraiEtAl2026c">G. Garai and N. Chamakuri, “Nonlinear Parareal-Incomplete OSWR Method for the Coupled Reaction-Diffusion System: Convergence Analysis and Computational Strategies,” arXiv:2607.02780v1 [math.NA], 2026 [Online]. Available at: <a href="https://arxiv.org/abs/2607.02780v1" target="_blank">https://arxiv.org/abs/2607.02780v1</a></span>
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BibTeX entry <code>GaraiEtAl2026c</code>
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<pre class="abstract">@unpublished{GaraiEtAl2026c,
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author = {Garai, Gobinda and Chamakuri, Nagaiah},
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howpublished = {arXiv:2607.02780v1 [math.NA]},
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title = {Nonlinear Parareal-Incomplete OSWR Method for the Coupled Reaction-Diffusion System: Convergence Analysis and Computational Strategies},
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url = {https://arxiv.org/abs/2607.02780v1},
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year = {2026}
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This paper presents a development of a nonlinear extension of the Parareal-Incomplete Optimized Schwarz Waveform Relaxation (OSWR) method, aimed at efficiently simulating coupled reaction-diffusion systems, with particular attention to those encountered in cardiac electrophysiology. The strategy leverages the synergy of spatial and temporal decomposition to tackle the computational challenges of large-scale, nonlinear simulations. The proposed approach is accompanied by a comprehensive convergence analysis. Extensive numerical experiments confirm the convergence of the nonlinear Parareal-Incomplete OSWR method. The results showcase its robust convergence behavior across various space-time subdomains, underscoring the method’s reliability and effectiveness, especially in complex simulations involving multiple subdomains.
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