论文标题
分数二维热方程上的谎言对称性减少和光谱方法
Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation
论文作者
论文摘要
在本文中，提出了针对时空对流扩散分数差分方程的谎言对称分析，该方程是通过（2+1）自变量和一个因变量的riemann-liouville衍生物。我们发现使用谎言对称性的相似解决方案的分数差分方程的还原形式。发现一维最佳对称代数的最佳系统。我们通过基于伯恩斯坦的操作矩阵来介绍一种计算方法，以在某些初始条件下求解二维小数热方程。
In this paper, the Lie symmetry analysis is proposed for a space-time convection-diffusion fractional differential equations with the Riemann-Liouville derivative by (2+1) independent variables and one dependent variable. We find a reduction form of our governed fractional differential equation using the similarity solution of our Lie symmetry. One-dimensional optimal system of Lie symmetry algebras is found. We present a computational method via the spectral method based on Bernstein's operational matrices to solve the two-dimensional fractional heat equation with some initial conditions.
