Comparison of Time and Spatial Collocation Methods
for the Heat Equation
Jules Kouatchou
We combine a high-order compact finite difference scheme to approximate the
spatial derivatives and collocation techniques for the time component to
numerically solve the two dimensional heat equation.
We use two approaches to implement the time collocation methods.
The first one is based on an explicit computation of the coefficients
of polynomials and the second one relies on differential quadratures.
We also implement a spatial collocation method where differential quadratures
are utilized for spatial derivatives and an implicit scheme for marching in
time.
We compare all the three techniques by studying their merits and analyzing
their numerical performance.
Our experiments show that all of them achieve high accurate approximate
solution but the time collocation method with differential quadrature
offers (with respect to the one with explicit polynomials) less
computational complexity and a better efficiency.
All our computations, based on parallel algorithms, are carried out
on the CRAY SV1.