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A second order numerical method for singularly perturbed Volterra integro-differential equations with delay

   | 31 paź 2023

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This study deals with singularly perturbed Volterra integro-differential equations with delay. Based on the properties of the exact solution, a hybrid difference scheme with appropriate quadrature rules on a Shishkin-type mesh is constructed. By using the truncation error estimate techniques and a discrete analogue of Grönwall’s inequality it is proved that the hybrid finite difference scheme is almost second order accurate in the discrete maximum norm. Numerical experiments support these theoretical results and indicate that the estimates are sharp.

eISSN:
2956-7068
Język:
Angielski
Częstotliwość wydawania:
2 razy w roku
Dziedziny czasopisma:
Computer Sciences, other, Engineering, Introductions and Overviews, Mathematics, General Mathematics, Physics