NEW CONSTRUCTION OF HIGHER-ORDER LOCAL CONTINUOUS PLATFORMS FOR ERROR CORRECTION METHODS | Zendy

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NEW CONSTRUCTION OF HIGHER-ORDER LOCAL CONTINUOUS PLATFORMS FOR ERROR CORRECTION METHODS

Author(s) -

Sunyoung Bu

Publication year - 2016

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2016033

Subject(s) - residual , mathematics , convergence (economics) , approximation error , order (exchange) , first order , initial value problem , order of accuracy , value (mathematics) , construct (python library) , rate of convergence , differential equation , mathematical analysis , mathematical optimization , algorithm , computer science , statistics , telecommunications , method of characteristics , channel (broadcasting) , finance , programming language , economics , economic growth

Error correction method (ECM) (6, 7) which has been recently de- veloped, 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 ), provid- ed 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 dierential 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 fth order Runge-Kutta methods. Numerical experiments demonstrate the theoretical results.

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