A second order difference scheme on a Bakhvalov-type mesh for the singularly perturbed Volterra delay-integro-differential equation

In this paper, we present a second order parameter-uniform numerical method for a singularly perturbed Volterra delay-integro-differential equation on a Bakhvalov-type mesh. The equation is discretized by using the variable two-step backward differentiation formula of the first derivative term and t...

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Veröffentlicht in:Computational & applied mathematics 2024-09, Vol.43 (6), Article 349
Hauptverfasser: Liao, Yige, Luo, Xianbing, Liu, Li-Bin
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we present a second order parameter-uniform numerical method for a singularly perturbed Volterra delay-integro-differential equation on a Bakhvalov-type mesh. The equation is discretized by using the variable two-step backward differentiation formula of the first derivative term and the trapezoidal formula of the integral term. The stability and convergence of the numerical method in the discrete maximum norm are proved. Finally, the theoretical results are verified by some numerical experiments.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-024-02873-6