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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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