DOAJ Open Access 2023

Approximate solutions to the Allen–Cahn equation using rational radial basis functions method

M. Shiralizadeh A. Alipanah M. Mohammadi

Lihat Sumber DOI

Abstrak

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.

Topik & Kata Kunci

Applied mathematics. Quantitative methods

Penulis (3)

M. Shiralizadeh

A. Alipanah

M. Mohammadi

Format Sitasi

APA MLA BibTeX

Shiralizadeh, M., Alipanah, A., Mohammadi, M. (2023). Approximate solutions to the Allen–Cahn equation using rational radial basis functions method. https://doi.org/10.22067/ijnao.2022.76010.1123

Akses Cepat

Lihat di Sumber doi.org/10.22067/ijnao.2022.76010.1123

Informasi Jurnal

Tahun Terbit: 2023
Sumber Database: DOAJ
DOI: 10.22067/ijnao.2022.76010.1123
Akses: Open Access ✓