scholarly journals Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

2009 ◽  
Vol 231 (1) ◽  
pp. 160-176 ◽  
Author(s):  
F. Liu ◽  
C. Yang ◽  
K. Burrage
Keyword(s):  
Numerical Method ◽  
Source Term ◽  
Nonlinear Source ◽  
Analytical Technique ◽  
Subdiffusion Equation

scholarly journals Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Qianqian Yang ◽  
Fawang Liu ◽  
Ian Turner
Keyword(s):  
Fractional Derivative ◽  
Numerical Method ◽  
Source Term ◽  
Planck Equation ◽  
Stability And Convergence ◽  
Nonlinear Source ◽  
Transport Dynamics ◽  
Time Space ◽  
Fokker Planck Equations ◽  
Fokker Planck

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPENST), which involve the Caputo time fractional derivative (CTFD) of order (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order (1, 2]. Approximating the CTFD and RSFD using the L1-algorithm and shifted Grünwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

scholarly journals Numerical method of identification of an unknown source term in a heat equation

2002 ◽  
Vol 8 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Afet Golayoğlu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Method ◽  
Minimization Problem ◽  
Unknown Function ◽  
Source Term ◽  
Numerical Procedure ◽  
Numerical Examples ◽  
Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

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