Piecewise Polynomial Collocation Methods for Fractional Differential Equations

被引：0

作者：

Pedas, Arvet ^{[1
]}

Tamme, Enn ^{[1
]}

机构：

[1] Univ Tartu, Inst Math, EE-50409 Tartu, Estonia

来源：

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III | 2010年 / 1281卷

关键词：

Fractional differential equation; Caputo derivative; Volterra integral equation; spline collocation method; graded grid; INTEGRODIFFERENTIAL EQUATIONS;

D O I：

暂无

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The numerical solution of initial value problems for linear fractional differential equations is considered. The derivatives of the given functions may be unbounded at the initial point of the interval of integration. Using an integral equation reformulation and special graded grids, global convergence estimates are derived and a collection of numerical results is given.

引用

页码：1203 / 1206

页数：4

共 50 条

[1] Adaptive methods for piecewise polynomial collocation for ordinary differential equations
Wright, K.
BIT NUMERICAL MATHEMATICS, 2007, 47 (01) : 197 - 212
[2] Adaptive methods for piecewise polynomial collocation for ordinary differential equations
K. Wright
BIT Numerical Mathematics, 2007, 47 : 197 - 212
[3] Piecewise polynomial collocation for linear boundary value problems of fractional differential equations
Pedas, Arvet
Tamme, Enn
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (13) : 3349 - 3359
[4] A Piecewise Nonpolynomial Collocation Method for Fractional Differential Equations
Esmaeili, Shahrokh
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2017, 12 (05):
[5] COLLOCATION METHODS FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE LINEAR DELAYS
Liang, Hui
Brunner, Hermann
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2012, 11 (05) : 1839 - 1857
[6] On the convergence of piecewise polynomial collocation methods for variable-order space-fractional diffusion equations
Yuan, Wenping
Liang, Hui
Chen, Yanping
MATHEMATICS AND COMPUTERS IN SIMULATION, 2023, 209 : 102 - 117
[7] Stability of piecewise polynomial collocation for Volterra integro-differential equations
Oja, P.
Tarang, M.
Mathematical Modelling and Analysis, 2001, 6 (02) : 310 - 320
[8] A polynomial collocation method for a class of singular fractional differential equations
Khan, Ghulam Abbas
Latt, Kaido
Rebelo, Magda
APPLIED NUMERICAL MATHEMATICS, 2025, 207 : 45 - 57
[9] Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels
Brunner, H
Pedas, A
Vainikko, G
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2001, 39 (03) : 957 - 982
[10] Improvement of the piecewise polynomial collocation method for Fredholm integro-differential equations
Parvaz, R.
Zarebnia, M.
Bagherzadeh, A. Saboor
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2025, 43

← 1 2 3 4 5 →