| Volume 6, Number 2, 2016, Pages 443-462 DOI：10.11948/2016033 |
| New construction of higher-order local continuous platformsfor Error Correction Methods |
| Sunyoung Bu |
| Keywords:Error correction method, local platform,
stiff initial value problem, Runge Kutta methods |
| Abstract: |
| Error correction method (ECM)~\cite{kim2011a,kim2011b} which has been
recently developed, is based on the construction of a local
approximation to the solution on each time step, and has the
excellent convergence order $O(h^{2p+2})$, provided the local
approximation has a local residual error $O(h^p)$.
In this paper, we construct a higher-order continuous local platform
to develop higher-order semi-explicit one-step ECM for solving initial
value time dependent differential equations. It is shown that special
choices of parameters for the local platform can lead to
the improvement of the well-known explicit fourth and fifth order
Runge-Kutta methods. Numerical experiments demonstrate
the theoretical results |
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