Adaptive High-Order Spectral Methods for Nonlinear Partial Differential  Equations

Ammar Turki Chyad

Adaptive High-Order Spectral Methods for Nonlinear Partial Differential Equations

Authors

Ammar Turki Chyad

Keywords:

Nonlinear PDEs, Spectral methods, Adaptive refinement, Fractional models, Numerical simulation

Abstract

Nonlinear partial differential equations (NPDEs) form the core of contemporary science andengineering, governing phenomena such as turbulence and anomalous diffusion, nonlinear wavepropagation, and multi-scale biological transport. Their very nature, often involving localized structures, fractional dynamics, and nonlocal interactions

References

H. K. Smith, High-Order Spectral and Pseudo-Spectral Methods for Solving Nonlinear Partial Differential Equations, 2025.

I. Ullah, K. Shah, and T. Abdeljawad, “Study of traveling soliton and fronts phenomena in

fractional Kolmogorov–Petrovskii–Piskunov equation,” Physica Scripta, vol. 99, no. 5, p. 055259, 2024.

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Published

2025-08-31

How to Cite

Ammar Turki Chyad. (2025). Adaptive High-Order Spectral Methods for Nonlinear Partial Differential Equations . Journal of Computational Analysis and Applications (JoCAAA), 34(8), 179–191. Retrieved from https://www.eudoxuspress.com/index.php/pub/article/view/3573