مشخصات پژوهش

عنوان	Approximate solutions to the Allen–Cahn equation using rational radial basis functions method
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	Allen–Cahn equation, RBFs, Rational RBFs method, Runge– Kutta method
چکیده	We apply the rational radial basis functions (RRBFs) method to solve the Allen–Cahn (A.C) equation, particularly when the equation has a solution with steep front or sharp gradients. We approximate the spatial derivatives by the RRBFs method. Then we apply an explicit, fourthorder 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 accuracy of the proposed method are provided.
پژوهشگران	مریم محمدی (نفر سوم)، امجد علی پناه (نفر دوم)، منصور شیرعلیزاده (نفر اول)