OPTIMAL ERROR ESTIMATES OF SPECTRAL PETROV-GALERKIN AND COLLOCATION METHODS FOR INITIAL VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS

被引：38

作者：

Zhang, Zhongqiang ^{[1
]}

Zeng, Fanhai ^{[2
]}

Karniadakis, George Em ^{[2
]}

机构：

[1] Worcester Polytech Inst, Dept Math Sci, Worcester, MA 01609 USA

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2015年 / 53卷 / 04期

关键词：

end-point singularity; spectral Petrov-Galerkin; collocation; error estimate; Jacobi polynomials; Laguerre polynomials; DIFFUSION EQUATION; UNBOUNDED-DOMAINS; ELEMENT METHODS; SPACE; APPROXIMATIONS; POLYNOMIALS; ORDER;

D O I：

10.1137/140988218

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present optimal error estimates for spectral Petrov-Galerkin methods and spectral collocation methods for linear fractional ordinary differential equations with initial value on a finite interval. We also develop Laguerre spectral Petrov-Galerkin methods and collocation methods for fractional equations on the half line. Numerical results confirm the error estimates.

引用

页码：2074 / 2096

页数：23

共 50 条

[31] Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative
Wei, Zhongli
Li, Qingdong
Che, Junling
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 367 (01) : 260 - 272
[32] A COLLOCATION METHOD FOR DIRECT NUMERICAL INTEGRATION OF INITIAL VALUE PROBLEMS IN HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS
Adeniyi, R. B.
Alabi, M. O.
ANALELE STIINTIFICE ALE UNIVERSITATII AL I CUZA DIN IASI-SERIE NOUA-MATEMATICA, 2011, 57 (02): : 311 - 321
[33] Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations
Guo, Ben-yu
Yan, Han-ping
APPLIED NUMERICAL MATHEMATICS, 2009, 59 (06) : 1386 - 1408
[34] Blow-up of error estimates in time-fractional initial-boundary value problems
Chen, Hu
Stynes, Martin
IMA JOURNAL OF NUMERICAL ANALYSIS, 2021, 41 (02) : 974 - 997
[35] Optimal Control of Positive Solution to Initial Value Problem for Fractional Integro-differential Equations
Zhang, Yongjie
Zhang, Lingling
2017 29TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC), 2017, : 7851 - 7856
[36] PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS
Liu, Yuji
ACTA MATHEMATICA SCIENTIA, 2016, 36 (05) : 1492 - 1508
[37] The Mixed Boundary Value Problems and Chebyshev Collocation Method for Caputo-Type Fractional Ordinary Differential Equations
Duan, Jun-Sheng
Jing, Li-Xia
Li, Ming
FRACTAL AND FRACTIONAL, 2022, 6 (03)
[38] ERROR ESTIMATES OF HIGH-ORDER NUMERICAL METHODS FOR SOLVING TIME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS
Li, Zhiqiang
Yan, Yubin
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (03) : 746 - 774
[39] Existence, uniqueness, and relaxation results in initial value type problems for nonlinear fractional differential equations
O. Baghani
S. M. S. Nabavi Sales
Analysis and Mathematical Physics, 2021, 11
[40] New Spectral Solutions of Multi-Term Fractional-Order Initial Value Problems With Error Analysis
Abd-Elhameed, W. M.
Youssri, Y. H.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2015, 105 (05): : 375 - 398

← 1 2 3 4 5 →