Volume 11, Issue 4 (2-2026)
mmr 2026, 11(4): 114-136 |
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Ayazi N. Numerical Solution of the Variable-Order Fractional Burger’s Equation Using a Hybrid Spectral Element Method with Adaptive Penalty Rate and Crank-Nicolson Leap-Frog Scheme. mmr 2026; 11 (4) :114-136
URL: http://mmr.khu.ac.ir/article-1-3458-en.html
URL: http://mmr.khu.ac.ir/article-1-3458-en.html
Abstract: (161 Views)
The primary objective of this study is to develop a hybrid numerical scheme for approximating the solutions of the one-dimensional fractional Burgers’ equation governed by a variable-order Riemann–Liouville derivative. In the proposed framework, spatial discretization is accomplished via a spectral element method based on the collocation approach, whereas temporal discretization is handled using a Crank–Nicolson Leap-Frog scheme. To enhance the stability of the derivative matrix resulting from the spectral element formulation, an adaptive penalty enforcement strategy is employed, wherein the penalty coefficient is dynamically adjusted in response to the local variations in the fractional derivative order. The accuracy, stability, and computational efficiency of the proposed method are validated through a series of numerical experiments, demonstrating its robustness and effectiveness across diverse test cases.
Keywords: Variable-Order Fractional Burger’s equation, Spectral Element Method, Adaptive Penalty, Crank-Nicolson Leap-Frog Scheme.
Type of Study: Original Manuscript |
Subject:
Anal
Received: 2025/10/4 | Revised: 2026/02/26 | Accepted: 2025/12/21 | Published: 2026/02/26 | ePublished: 2026/02/26
Received: 2025/10/4 | Revised: 2026/02/26 | Accepted: 2025/12/21 | Published: 2026/02/26 | ePublished: 2026/02/26
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