Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
- Kouatchou, Jules
- Physical Description:
- 1 electronic document
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- In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
- NASA Technical Reports Server (NTRS) Collection.
- Document ID: 20000024883.
- No Copyright.
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