Conference abstracts

Session B7 - Numerical Linear Algebra

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Fast numerical solver for higher order local platforms based on error correction methods

Sunyoung Bu

Hongik University, South Korea   -   syboo@hongik.ac.kr

Error correction method (ECM) [1,2] is based on the construction of a local approximation to the solution on each time step. In this study, a higher-order continuous local platform is constructed to develop higher-order semi-explicit one-step ECM due to the excellent convergence order $O(h^{2p+2})$ of ECM, provided the local approximation has a local residual error $O(h^p)$. Unfortunately, the construction generates inevitably a huge size of matrix. To overcome this complexity, a fast numerical matrix solver is also provided. 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.

[1] P. Kim, X. Piao and S.D. Kim, An error corrected Euler method for solving stiff problems based on Chebyshev collocation, SIAM J. Numer. Anal., 49(2011), 2211--2230.

[2] S.D. Kim, X. Piao, D.H. Kim and P. Kim, Convergence on error correction methods for solving initial value problems, J. Comp. Appl. Math., 236(2012)(17), 4448--4461.

Joint work with Philsu Kim (Kyungpook National University, South Korea).

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