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
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
收藏
页数:18
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