Numerical simulations of nonlinear stochastic Newell-Whitehead-Segel equation and its measurable properties

MS Iqbal, MW Yasin, N Ahmed, A Akg�l, M Rafiq…�- …�of Computational and�…, 2023 - Elsevier
Journal of Computational and Applied Mathematics, 2023Elsevier
In this article, the stochastic form of the Newell-Whitehead-Segel equation has been
investigated. This is a fully nonlinear partial differential equation and has huge applications.
The nonlinearity of the underlying problem leads to the fact that one has to do the nonlinear
analysis of the problem. So, firstly this article describes the regularity of the solution in the
context of existing theory and a new approach has been applied to show the existence of the
solution and corresponding explicit a-priori estimates of the Schauder type have been�…
Abstract
In this article, the stochastic form of the Newell-Whitehead-Segel equation has been investigated. This is a fully nonlinear partial differential equation and has huge applications. The nonlinearity of the underlying problem leads to the fact that one has to do the nonlinear analysis of the problem. So, firstly this article describes the regularity of the solution in the context of existing theory and a new approach has been applied to show the existence of the solution and corresponding explicit a-priori estimates of the Schauder type have been proposed. Secondly, in the next part, we have proposed two numerical schemes for the solution of the underlying problem and both schemes are very fighting for consistency and stability. The obtained numerical results are reliable, time-efficient, and very much adjacent to the exact state of the unknown function.
Elsevier
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