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Kafkas Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Kars
Abstract
This paper presents an implicit exponential finite difference method specifically developed for solving the time-fractional Newell–Whitehead–Segel (NWS) equation, where the conformable fractional derivative is taken into account. Von Neumann stability analysis is employed to evaluate the stability of the proposed numerical scheme. Due to the implicit nature of the scheme, each temporal iteration leads to a system of nonlinear equations. These systems are linearized using Newton's method, facilitating their numerical resolution. To validate the accuracy of the method, numerical results are benchmarked against known exact solutions. The simulation results show that the proposed method is accurate and reliable for solving the complex structure of the time-fractional NWS equation.
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