Existence and blow-up of solutions to the fractional stochastic heat equations

2017 ◽  
Vol 6 (1) ◽  
pp. 73-108
Author(s):  
Pavel Bezdek
Keyword(s):  
Blow Up ◽  
Heat Equations ◽  
Stochastic Heat Equations

scholarly journals Some properties of non-linear fractional stochastic heat equations on bounded domains

2017 ◽  
Vol 102 ◽  
pp. 86-93 ◽  
Author(s):  
Mohammud Foondun ◽  
Ngartelbaye Guerngar ◽  
Erkan Nane
Keyword(s):  
Heat Equations ◽  
Bounded Domains ◽  
Non Linear ◽  
Stochastic Heat Equations

scholarly journals A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 904 ◽  
Author(s):  
Afshin Babaei ◽  
Hossein Jafari ◽  
S. Banihashemi
Keyword(s):  
Order Of Convergence ◽  
Additive Noise ◽  
Numerical Solutions ◽  
Numerical Test ◽  
Test Problems ◽  
Heat Equations ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Stochastic Heat Equations ◽  
Collocation Approach

A spectral collocation approach is constructed to solve a class of time-fractional stochastic heat equations (TFSHEs) driven by Brownian motion. Stochastic differential equations with additive noise have an important role in explaining some symmetry phenomena such as symmetry breaking in molecular vibrations. Finding the exact solution of such equations is difficult in many cases. Thus, a collocation method based on sixth-kind Chebyshev polynomials (SKCPs) is introduced to assess their numerical solutions. This collocation approach reduces the considered problem to a system of linear algebraic equations. The convergence and error analysis of the suggested scheme are investigated. In the end, numerical results and the order of convergence are evaluated for some numerical test problems to illustrate the efficiency and robustness of the presented method.

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