On the numerical solution of the iterative parabolic equations by ETDRK pseudospectral methods in linear and nonlinear media

2022 ◽  
pp. 106228
Author(s):  
Sergey B. Kozitskiy ◽  
Mikhail Yu. Trofimov ◽  
Pavel S. Petrov
Keyword(s):  
Numerical Solution ◽  
Parabolic Equations ◽  
Pseudospectral Methods ◽  
Nonlinear Media ◽  
Linear And Nonlinear

Numerical solution of the Maxwell equations in nonlinear media

1996 ◽  
Vol 32 (3) ◽  
pp. 950-953
Author(s):  
G. Miano ◽  
C. Serpico ◽  
L. Verolino ◽  
F. Villone
Keyword(s):  
Numerical Solution ◽  
Maxwell Equations ◽  
Nonlinear Media

scholarly journals An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Khalid Atifi ◽  
Idriss Boutaayamou ◽  
Hamed Ould Sidi ◽  
Jawad Salhi
Keyword(s):  
Numerical Solution ◽  
Parabolic Equations ◽  
Measurement Data ◽  
Gradient Methods ◽  
Stability Estimate ◽  
Inverse Source Problem ◽  
Output Least Squares ◽  
Singular Parabolic Equations ◽  
Interior Degeneracy ◽  
Least Squares Approach

The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additional measurement data are given on a suitable interior subdomain. For the numerical solution, the reconstruction is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. The Fréchet differentiability of the Tikhonov functional and the Lipschitz continuity of the Fréchet gradient are proved. These properties allow us to apply gradient methods for numerical solution of the considered inverse source problem.

scholarly journals Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Dumitru Baleanu
Keyword(s):  
Parabolic Equation ◽  
Fractional Calculus ◽  
Numerical Solution ◽  
Parabolic Equations ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Implicit Schemes ◽  
The Stability

A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.

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