TY - JOUR
T1 - An embedded formula of the Chebyshev collocation method for stiff problems
AU - Piao, Xiangfan
AU - Bu, Sunyoung
AU - Kim, Dojin
AU - Kim, Philsu
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/12/15
Y1 - 2017/12/15
N2 - In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge–Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.
AB - In this study, we have developed an embedded formula of the Chebyshev collocation method for stiff problems, based on the zeros of the generalized Chebyshev polynomials. A new strategy for the embedded formula, using a pair of methods to estimate the local truncation error, as performed in traditional embedded Runge–Kutta schemes, is proposed. The method is performed in such a way that not only the stability region of the embedded formula can be widened, but by allowing the usage of larger time step sizes, the total computational costs can also be reduced. In terms of concrete convergence and stability analysis, the constructed algorithm turns out to have an 8th order convergence and it exhibits A-stability. Through several numerical experimental results, we have demonstrated that the proposed method is numerically more efficient, compared to several existing implicit methods.
KW - Collocation method
KW - Embedded formula
KW - Generalized Chebyshev polynomial
KW - Stiff initial value problem
UR - http://www.scopus.com/inward/record.url?scp=85030453210&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2017.09.046
DO - 10.1016/j.jcp.2017.09.046
M3 - Article
AN - SCOPUS:85030453210
SN - 0021-9991
VL - 351
SP - 376
EP - 391
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -