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 introduces an approach to decoupling singularly perturbed boundaryvalue problems for fourth-order ordinary differential equations that feature asmall positive parameter $\epsilon$ multiplying the highest derivative. Wespecifically examine Lidstone boundary conditions and demonstrate how to breakdown fourth-order differential equations into a system of second-orderproblems, with one lacking the parameter and the other featuring $\epsilon$multiplying the highest derivative. To solve this system, we propose a mixedfinite element algorithm and incorporate the Shishkin mesh scheme to capturethe solution near boundary layers. Our solver is both direct and of highaccuracy, with computation time that scales linearly with the number of gridpoints. We present numerical results to validate the theoretical results andthe accuracy of our method.

A Mixed Finite Element Method for Singularly Perturbed Fourth Oder Convection-Reaction-Diffusion Problems on Shishkin Mesh