High-Order Schemes and Collocation Methods
We combine high-order schemes and collocation methods to solve evolution
problems such as the heat equation and the wave equation.
The method, called implicit collocation method (ICM), is unconditionally stable.
Its principle is as follows: after discretization in space of the problem,
the solution is approximated at each spatial grid point by a polynomial
depending of time.
The resulting derivation produces a linear system of equations.
The order of ICM is in space the order of the difference approximation
and in time the degree of the polynomial.
One of the main advantages of ICM is that it allows
parallelization across both time and space.
Selected Publications
- Jules Kouatchou, Finite differences and collocation methods for
the two dimensional heat equation,
to appear in Numerical Methods for PDEs.
- Jules Kouatchou, Parallel implementation of a high-order implicit
collocation method for the heat equation,
Mathematics and Computers in Simulation,
Vol. 54, no. 6, p. 509-519 (2001).
- Jules Kouatchou,
Comparison of time and spatial collocation methods for the heat
equation,
Journal of Computational and Applied Mathematics, Vol. 150, No. 1,
p. 129-141 (2003).
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