English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper aims at obtaining, by means of integral transforms, analyticalapproximations in short times of solutions to boundary value problems for theone-dimensional reaction-diffusion equation with constant coefficients. Thegeneral form of the equation is considered on a bounded generic interval andthe three classical types of boundary conditions, i.e., Dirichlet as well asNeumann and mixed boundary conditions are considered in a unified way. TheFourier and Laplace integral transforms are successively applied and an exactsolution is obtained in the Laplace domain. This operational solution is provento be the accurate Laplace transform of the infinite series obtained by theFourier decomposition method and presented in the literature as solutions tothis type of problem. On the basis of this unified operational solution, fourcases are distinguished where innovative formulas expressing consistentanalytical approximations in short time limits are derived with respect to thebehavior of the solution at the boundaries. Compared to the infinite seriessolutions, the analytical approximations may open new perspectives andapplications, among which can be noted the improvement of numerical efficiencyin simulations of one-dimensional moving boundary problems, such as in Stefanmodels.

Analytical approximations in short times of exact operational solutions to reaction diffusion problems on bounded intervals