Approximate solutions to the Allen–Cahn equation using rational radial basis functions method
عنوان مقاله: Approximate solutions to the Allen–Cahn equation using rational radial basis functions method
شناسه ملی مقاله: JR_IJNAO-13-2_003
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_IJNAO-13-2_003
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
M. Shiralizadeh - Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran.
A. Alipanah - Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran.
M. Mohammadi - Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.
خلاصه مقاله:
M. Shiralizadeh - Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran.
A. Alipanah - Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran.
M. Mohammadi - Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.
We apply the rational radial basis functions (RRBFs) method to solve the Allen–Cahn (A.C) equation, particularly when the equation has a so-lution with steep front or sharp gradients. We approximate the spatial derivatives by the RRBFs method. Then we apply an explicit, fourth-order Runge–Kutta method to advance the resulting semi-discrete system in time. It is well known that the A.C equation has a nonlinear stability feature, meaning that the free-energy functional is reduced by time. The presented method maintains the total energy reduction property of the A.C equation. In the end, five examples to confirm the efficiency and accuracyof the proposed method are provided.
کلمات کلیدی: Allen–Cahn equation, RBFs, Rational RBFs method, Runge–Kutta method
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1685435/