scholarly journals Linearization Method of Nonlinear Source Term.

1993 ◽  
Vol 59 (559) ◽  
pp. 827-832
Author(s):  
Takeo Maeda
Keyword(s):  
Source Term ◽  
Linearization Method ◽  
Nonlinear Source

scholarly journals Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Y. J. Choi ◽  
S. K. Chung
Keyword(s):  
Finite Element ◽  
Diffusion Equation ◽  
Fractional Derivative ◽  
Source Term ◽  
Approximate Solutions ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Nonlinear Source ◽  
Backward Euler ◽  
Space Fractional Diffusion Equation

We consider finite element Galerkin solutions for the space fractional diffusion equation with a nonlinear source term. Existence, stability, and order of convergence of approximate solutions for the backward Euler fully discrete scheme have been discussed as well as for the semidiscrete scheme. The analytical convergent orders are obtained asO(k+hγ˜), whereγ˜is a constant depending on the order of fractional derivative. Numerical computations are presented, which confirm the theoretical results when the equation has a linear source term. When the equation has a nonlinear source term, numerical results show that the diffusivity depends on the order of fractional derivative as we expect.

scholarly journals Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3050
Author(s):  
Sarita Nandal ◽  
Mahmoud A. Zaky ◽  
Rob H. De Staelen ◽  
Ahmed S. Hendy
Keyword(s):  
Fourth Order ◽  
Numerical Scheme ◽  
Source Term ◽  
Variable Coefficients ◽  
Second Order ◽  
Order Accuracy ◽  
Nonlinear Source ◽  
Second Order In Time ◽  
Convergence Orders ◽  
Temporal Direction

The purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using the L2−1σ approximation of the time Caputo derivative, a finite difference method with second-order accuracy in the temporal direction is achieved. The novelty of this paper is to introduce a numerical scheme for the problem under consideration with variable coefficients, nonlinear source term, and delay time constant. The numerical results show that the global convergence orders for spatial and time dimensions are approximately fourth order in space and second-order in time.

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