An Efficient Spline Collocation Method for a Nonlinear Fourth-Order Reaction Subdiffusion Equation

被引：23

作者：

Zhang, Haixiang ^{[1
]}

Yang, Xuehua ^{[1
]}

Xu, Da ^{[2
]}

机构：

[1] Hunan Univ Technol, Sch Sci, Zhuzhou 412007, Peoples R China

[2] Hunan Normal Univ, Dept Math, Changsha 410081, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2020年 / 85卷 / 01期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Fourth-order time fractional equation; Finite difference method; Collocation scheme; Convergence; PARTIAL-DIFFERENTIAL-EQUATIONS; BOUNDARY-VALUE-PROBLEMS; ERROR ANALYSIS; TIME; SCHEME;

D O I：

10.1007/s10915-020-01308-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The nonlinear fourth-order reaction-subdiffusion equation whose solutions display a typical initial weak singularity is considered. A new analytical technique is introduced to analyze orthogonal spline collocation (OSC) method based on L1 scheme on graded mesh. By introducing a discrete convolution kernel and discrete fractional Gronwall inequality, convergence of the scheme is proved rigorously. This novel analytical technique can provide new insights in analyzing other time fractional fourth-order differential equations with weakly singular solutions.

引用

页数：18

共 34 条

[1] Existence of nontrivial solutions of an asymptotically linear fourth-order elliptic equation [J].

An, Yukun ;

Liu, Renyi .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (11) :3325-3331

[2] Superconvergence Points for the Spectral Interpolation of Riesz Fractional Derivatives [J].

Deng, Beichuan ;

Zhang, Zhimin ;

Zhao, Xuan .

JOURNAL OF SCIENTIFIC COMPUTING, 2019, 81 (03) :1577-1601

[3]

Douglas Jr, 1974, LECT NOTES MATH, V385

[4] Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation [J].

Du, Yanwei ;

Liu, Yang ;

Li, Hong ;

Fang, Zhichao ;

He, Siriguleng .

JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 344 :108-126

[5] An Exponentially Convergent Scheme in Time for Time Fractional Diffusion Equations with Non-smooth Initial Data [J].

Duan, Beiping ;

Zheng, Zhoushun .

JOURNAL OF SCIENTIFIC COMPUTING, 2019, 80 (02) :717-742

[6]

Fairweather G., 1993, Num. Meth. for PDE's, V9, P191, DOI DOI 10.1002/NUM.1690090207

[7] An ADI Crank-Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation [J].

Fairweather, Graeme ;

Yang, Xuehua ;

Xu, Da ;

Zhang, Haixiang .

JOURNAL OF SCIENTIFIC COMPUTING, 2015, 65 (03) :1217-1239

[8] An Improved Algorithm Based on Finite Difference Schemes for Fractional Boundary Value Problems with Nonsmooth Solution [J].

Hao, Zhaopeng ;

Cao, Wanrong .

JOURNAL OF SCIENTIFIC COMPUTING, 2017, 73 (01) :395-415

[9] Numerical Schemes for Solving the Time-Fractional Dual-Phase-Lagging Heat Conduction Model in a Double-Layered Nanoscale Thin Film [J].

Ji, Cui-cui ;

Dai, Weizhong ;

Sun, Zhi-zhong .

JOURNAL OF SCIENTIFIC COMPUTING, 2019, 81 (03) :1767-1800

[10] Numerical Algorithms with High Spatial Accuracy for the Fourth-Order Fractional Sub-Diffusion Equations with the First Dirichlet Boundary Conditions [J].

Ji, Cui-cui ;

Sun, Zhi-zhong ;

Hao, Zhao-peng .

JOURNAL OF SCIENTIFIC COMPUTING, 2016, 66 (03) :1148-1174

← 1 2 3 4 →