A new method based on Legendre polynomials for solutions of the fractional two-dimensional heat conduction equation

作者：Khalil Hammad^*; Khan Rahmat Ali

来源：Computers & Mathematics with Applications, 2014, 67(10): 1938-1953.

DOI：10.1016/j.camwa.2014.03.008

• Legendre polynomials
• Fractional partial differential equations
• Operational matrices of integration
• Numerical simulation
• Two-dimensional heat conduction equation

In this paper, we develop a new scheme for numerical solutions of the fractional two-dimensional heat conduction equation on a rectangular plane. Our main aim is to generalize the Legendre operational matrices of derivatives and integrals to the three dimensional case. By the use of these operational matrices, we reduce the corresponding fractional order partial differential equations to a system of easily solvable algebraic equations. The method is applied to solve several problems. The results we obtain are compared with the exact solutions and we find that the error is negligible.

• 出版日期2014-6