An efficient computational technique for semilinear time-fractional diffusion equation

被引:0
作者
Seal, Aniruddha [1 ]
Natesan, Srinivasan [1 ]
机构
[1] Indian Inst Technol, Dept Math, Gauhati 781039, Assam, India
关键词
k-Caputo fractional derivative; Tempered fractional derivative; Elzaki decomposition method; Stability; Error analysis; CONVERGENCE;
D O I
10.1007/s10092-024-00604-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this manuscript, we aim to study the semi-analytical and the numerical solution of a semilinear time-fractional diffusion equation where the time-fractional term includes the combination of tempered fractional derivative and k-Caputo fractional derivative with a parameter k >= 1. The application of the new integral transform, namely Elzaki transform of the temperedk-Caputo fractional derivative is shown here and there after the semi-analytical solution is obtained by using the Elzaki decomposition method. The model problem is linearized using Newton's quasilinearization method, and then the quasilinearized problem is discretized by the difference scheme namely tempered L-k(2)-1(sigma) method. Stability and convergence analysis of the proposed scheme have been discussed in the L-2-norm using the energy method. In support of the theoretical results, numerical example has been incorporated.
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页数:22
相关论文
共 26 条
[21]   Fractional Fourier transform as a signal processing tool: An overview of recent developments [J].
Sejdic, Ervin ;
Djurovic, Igor ;
Stankovic, Ljubisa .
SIGNAL PROCESSING, 2011, 91 (06) :1351-1369
[22]   Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method [J].
Shah, Rasool ;
Khan, Hassan ;
Mustafa, Saima ;
Kumam, Poom ;
Arif, Muhammad .
ENTROPY, 2019, 21 (06)
[23]   Local discontinuous Galerkin methods for the time tempered fractional diffusion equation [J].
Sun, Xiaorui ;
Li, Can ;
Zhao, Fengqun .
APPLIED MATHEMATICS AND COMPUTATION, 2020, 365
[24]   The numerical simulation of the tempered fractional Black-Scholes equation for European double barrier option [J].
Zhang, H. ;
Liu, F. ;
Turner, I. ;
Chen, S. .
APPLIED MATHEMATICAL MODELLING, 2016, 40 (11-12) :5819-5834
[25]  
Zhao L, 2016, MATH COMP
[26]   Linearized finite difference schemes for a tempered fractional Burgers equation in fluid-saturated porous rocks [J].
Zhao, Le ;
Zhao, Fengqun ;
Li, Can .
WAVES IN RANDOM AND COMPLEX MEDIA, 2021, :2816-2840