COMPARISON BETWEEN SOLUTIONS OF A TWO-DIMENSIONAL TIME-FRACTIONAL DIFFUSION-REACTION EQUATION THROUGH LIE SYMMETRIES

被引:0
作者
Jannelli, Alessandra [1 ]
Speciale, Maria Paola [1 ]
机构
[1] Univ Messina, Dipartimento Sci Matemat & Informat Sci Fis & Sci, Viale F Stagno dAlcontres 31, Messina, Italy
来源
ATTI ACCADEMIA PELORITANA DEI PERICOLANTI-CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI | 2021年 / 99卷 / 01期
关键词
FINITE-VOLUME METHOD; DIFFERENTIAL-EQUATIONS; NUMERICAL-SOLUTIONS; SYSTEM; ORDER;
D O I
10.1478/AAPP.991A4
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this paper, exact and numerical solutions of two dimensional time-fractional diffusion-reaction equation involving the Riemann-Liouville derivative are determined, by applying a procedure that combines the Lie symmetry analysis with the numerical methods. Two new reduced fractional differential equations are obtained by using the Lie symmetry theory. Applying only one Lie transformation, we get a new time-fractional partial differential equation and, applying a further Lie transformation, we get an ordinary differential equation. Numerical solutions of the reduced differential equations are computed separately by implicit numerical methods. A comparative study between numerical solutions is performed.
引用
收藏
页数:18
相关论文
共 56 条
[1]  
[Anonymous], 1995, CRC HDB LIE GROUP AN
[2]  
Bluman G.W., 1989, SYMMETRIES DIFFERENT, P1, DOI DOI 10.1007/978-1-4757-4307-4
[3]   Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations [J].
Buckwar, E ;
Luchko, Y .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 227 (01) :81-97
[4]   Solution to the Linear Fractional Differential Equation Using Adomian Decomposition Method [J].
Cheng, Jin-Fa ;
Chu, Yu-Ming .
MATHEMATICAL PROBLEMS IN ENGINEERING, 2011, 2011
[5]   Adomian decomposition: a tool for solving a system of fractional differential equations [J].
Daftardar-Gejji, V ;
Jafari, H .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 301 (02) :508-518
[6]  
Diethelm K., 2010, The Analysis of Fractional Dierential Equations, P247, DOI DOI 10.1007/978-3-642-14574-2
[7]   Finite difference/collocation method to solve multi term variable-order fractional reaction-advection-diffusion equation in heterogeneous medium [J].
Dwivedi, Kushal Dhar ;
Rajeev ;
Das, S. ;
Gomez-Aguilar, Jose Francisco .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2021, 37 (03) :2031-2045
[8]   Numerical Solution of Nonlinear Space-Time Fractional-Order Advection-Reaction-Diffusion Equation [J].
Dwivedi, Kushal Dhar ;
Rajeev ;
Das, Subir ;
Baleanu, Dumitru .
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2020, 15 (06)
[9]   A Finite Difference Method on Non-Uniform Meshes for Time-Fractional Advection-Diffusion Equations with a Source Term [J].
Fazio, Riccardo ;
Jannelli, Alessandra ;
Agreste, Santa .
APPLIED SCIENCES-BASEL, 2018, 8 (06)
[10]   A finite volume method for two-dimensional Riemann-Liouville space-fractional diffusion equation and its efficient implementation [J].
Fu, Hongfei ;
Liu, Huan ;
Wang, Hong .
JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 388 :316-334