In this research, a new second-order finite difference scheme is proposed to solve two and three- dimensional heat equation. Finite difference equations are determined via a discretization approach in which spatial second order partial derivatives in x and y directions are approximated simultaneously while in the classic method, each spatial partial derivative is replaced by a central finite difference approximation, separately. By this new discretization scheme and also using the forward difference to the first-order time derivative, a finite difference equation is obtained for the parabolic equation. This approach is explicit and similar to other explicit approaches, an interval for the Courant number, r is determined. This region for r is obtained through Fourier stability analysis. The advantage of this approach is that its stability interval is larger than the interval for traditional methods. Numerical experiments are presented to confirm the theoretical results. It is shown that more accurate approximations can be obtained by the new scheme.
Biazar, Jafar and Asayesh, Roxana
(R1458) A New Finite Difference Scheme for High-Dimensional Heat Equation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
2, Article 23.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss2/23