scholarly journals Numerical Studies of a Nonlinear Heat Equation With a Fractional Derivative

2021 ◽  
Vol 36 (2) ◽  
pp. 47-53
Author(s):  
V.D. Beybalaev ◽  
◽  
T.I. Ibavov ◽  
A.G. Omarova ◽  
◽  
...  
Keyword(s):  
Heat Equation ◽  
Fractional Derivative ◽  
Nonlinear Heat Equation ◽  
Numerical Studies

Similarity solutions and the computation formulas of a nonlinear fractional-order generalized heat equation

2019 ◽  
Vol 33 (10) ◽  
pp. 1950122 ◽  
Author(s):  
Yufeng Zhang
Keyword(s):  
Heat Equation ◽  
Fractional Derivative ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Nonlinear Heat Equation ◽  
Order Ordinary Differential Equation ◽  
Nonlinear Heat Conduction Equation ◽  
Liouville Fractional Derivative ◽  
Generalized Heat Equation ◽  
Two Parameters

A generalized nonlinear heat equation with the fractional derivative is proposed, whose similarity solutions are derived from a type of special scalar transformation with two parameters. With the help of separated variable method, two special series solutions of the standard heat equation are obtained. Finally, through computation of the left Riemann–Liouville fractional derivative, we obtain two approximated computation formulas of the factional-order ordinary differential equation which could be used to calculate the numerical solutions of the generalized nonlinear heat conduction equation.

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

scholarly journals Null controllability of a nonlinear heat equation

2002 ◽  
Vol 7 (7) ◽  
pp. 375-383 ◽  
Author(s):  
G. Aniculăesei ◽  
S. Aniţa
Keyword(s):  
Heat Equation ◽  
Dirichlet Boundary ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Nonlinear Heat Equation ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Linearized System ◽  
Kakutani Fixed Point ◽  
Exact Null Controllability ◽  
Kakutani Fixed Point Theorem

We study the internal exact null controllability of a nonlinear heat equation with homogeneous Dirichlet boundary condition. The method used combines the Kakutani fixed-point theorem and the Carleman estimates for the backward adjoint linearized system. The result extends to the case of boundary control.

Lie symmetries and invariants for a 2D nonlinear heat equation

2008 ◽  
Vol 68 (8) ◽  
pp. 2261-2268 ◽  
Author(s):  
Rodica Cimpoiasu ◽  
Radu Constantinescu
Keyword(s):  
Heat Equation ◽  
Lie Symmetries ◽  
Nonlinear Heat Equation

scholarly journals On exact solutions of the nonlinear heat equation

2019 ◽  
Vol 5 ◽  
pp. 11-17
Author(s):  
A.F. Barannyk ◽  
◽  
T.A. Barannyk ◽  
I.I. Yuryk ◽  
◽  
...  
Keyword(s):  
Heat Equation ◽  
Exact Solutions ◽  
Nonlinear Heat Equation
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