Finite Differences and Collocation Methods
for the two
Dimensional Heat Equation
Jules Kouatchou
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.