The G-functions Series Method Adapted to the Numerical Integration of Parabolic PDE
2018
The Method Of Lines (MOL) and Scheifele’s G-functions in the design of
algorithms adapted for the numeric integration of parabolic Partial
Differential Equations (PDE) in one space dimension are applied. The
semi-discrete system of ordinary differential equations in the time direction,
obtained by applying the MOL to PDE, is solved with the use of a method of Adapted
Series, based on Scheifele’s G-functions. This method
integrates exactly unperturbed linear systems of ordinary differential equations,
with only one G-function. An implementation
of this algorithm is used to approximate the solution of two test problems
proposed by various authors. The results obtained by the Dufort-Frankel, Crank-Nicholson
and the methods of Adapted Series versus the analytical solution, show the
results of mistakes made.
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