TY - JOUR
T1 - An enhanced Chebyshev collocation method based on the integration of Chebysehv interpolation
AU - Kim, Philsu
N1 - Publisher Copyright:
© Kyungpook Mathematical Journal.
PY - 2017
Y1 - 2017
N2 - In this paper, we develop an enhanced Chebyshev collocation method based on an integration scheme of the generalized Chebyshev interpolations for solving stiffinitial value problems. Unlike the former error embedded Chebyshev collocation method (CCM), the enhanced scheme calculates the solution and its truncation error based on the interpolation of the derivative of the true solution and its integration. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the 7th convergence order and the A-stability without any loss of advantages for CCM. Throughout a numerical result, we assess the proposed method is numerically more efficient compared to existing methods.
AB - In this paper, we develop an enhanced Chebyshev collocation method based on an integration scheme of the generalized Chebyshev interpolations for solving stiffinitial value problems. Unlike the former error embedded Chebyshev collocation method (CCM), the enhanced scheme calculates the solution and its truncation error based on the interpolation of the derivative of the true solution and its integration. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have the 7th convergence order and the A-stability without any loss of advantages for CCM. Throughout a numerical result, we assess the proposed method is numerically more efficient compared to existing methods.
KW - Collocation method
KW - Error embedded method
KW - Generalized Chebyshev polynomial
KW - Integration scheme
KW - Stiffinitial value problem
UR - http://www.scopus.com/inward/record.url?scp=85021913196&partnerID=8YFLogxK
U2 - 10.5666/KMJ.2017.57.2.287
DO - 10.5666/KMJ.2017.57.2.287
M3 - Article
AN - SCOPUS:85021913196
SN - 1225-6951
VL - 57
SP - 287
EP - 299
JO - Kyungpook Mathematical Journal
JF - Kyungpook Mathematical Journal
IS - 2
ER -