Numerical Solution to Inverse Source Problems for Linear Parabolic Equation

The aim of this work is to highlight that the adaptivity of the time step when combined with the adaptivity of the spectral mesh is optimal for a semi-linear parabolic equation discretized by an implicit Euler scheme in time and spectral elements method in space. The numerical results confirm the optimality of the order of convergence. The later is similar to the order of the error indicators.

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

Abstract and Applied Analysis ◽

10.1155/2013/828764 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 21

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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Numerical solution of the problem on reconstructing the initial condition for a semilinear parabolic equation

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/156939806777973391 ◽

2006 ◽

Vol 21 (4) ◽

Author(s):

E. I. Parmuzin ◽

V. P. Shutyaev

Keyword(s):

Parabolic Equation ◽

Numerical Solution ◽

Semilinear Parabolic Equation ◽

Initial Condition ◽

Semilinear Parabolic

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Controllability Property of a Superlinear Climate System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.367.264 ◽

2013 ◽

Vol 367 ◽

pp. 264-269

Author(s):

Liang Zhang ◽

Yang Liu

Keyword(s):

Fixed Point ◽

Parabolic Equation ◽

Fixed Point Theorem ◽

Point Theorem ◽

Point Of View ◽

Climate System ◽

Linear Parabolic Equation ◽

Controllability Property

This work concerns a climate system in the point of view of controllability. We obtain by the Kakutani’s fixed point theorem and the controllability property of the linear parabolic equation that the superlinear climate system is null controllable in the case with interior control.

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