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Spectral Optimized Multiderivative Hybrid Block Method for Fitzhugh–Nagumo Equations

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Gepubliceerd in:International Journal of Differential Equations vol. 2025 (2025)
Hoofdauteur: Rufai, Uthman O
Andere auteurs: Sibanda, Precious, Goqo, Sicelo P, Ahmedai, Salma A A, Adeyemo, Adeyinka S
Gepubliceerd in:
John Wiley & Sons, Inc.
Onderwerpen:
Basis functions
Accuracy
Methods
Stability
Numerical methods
Efficiency
Spectral methods
Collocation methods
Power series
Partial differential equations
Differential equations
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Samenvatting:The Fitzhugh–Nagumo equation, a key model for excitable systems in biology and neuroscience, requires efficient numerical methods due to its nonlinear nature. A spectral optimized multiderivative hybrid block method is proposed, constructed using a multistep collocation and interpolation technique with an approximated power series as the basis function. Incorporating two optimal intra-step points, the method demonstrates improved accuracy, with its consistency, convergence, and absolute stability rigorously analyzed. By combining the optimized multiderivative hybrid block method in time with a spectral collocation method in space, the approach demonstrates potency and flexibility in solving partial differential equations. Prior to using the spectral method, the partial differential equation is linearized using a linear partition technique. Numerical experiments confirm the accuracy and efficiency of the method compared to existing methods, demonstrating the potential of the method as a robust framework for solving partial differential equations requiring both high accuracy and stability.
ISSN:1687-9643
1687-9651
DOI:10.1155/ijde/1943008
Bron:Advanced Technologies & Aerospace Database