# Diagonally Multistep Block Method for Solving Volterra Integro-differential Equation with Delay

• Nur Auni Baharum Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor
• Zanariah Abdul Majid Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor
• Norazak Senu Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor
• Haliza Rosali Department of Mathematics and Statistics, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor

### Abstract

Volterra integro-differential equation with delay (VIDED) is solved using a diagonally multistep block method (DMB). This study provides the derivation of the DMB utilizing Taylor series with a constant step size strategy for treating the first order VIDED. In predictor-corrector mode, the DMB method combines the predictor and corrector formulae. It approximates two numerical solutions simultaneously within a block. The algorithm for the approximation solution is developed and the Newton-Cotes formulae are adapted in the DMB method to estimate the solution for an integral component. Theoretically, the consistency and zero stability that led to convergence properties are examined. The stability region also has been plotted. The numerical results indicate that the developed method is superior in terms of the number of steps, accuracy and computation time taken.

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Published
2023-11-19
How to Cite
BAHARUM, Nur Auni et al. Diagonally Multistep Block Method for Solving Volterra Integro-differential Equation with Delay. Menemui Matematik (Discovering Mathematics), [S.l.], v. 45, n. 2, p. 208-223, nov. 2023. ISSN 0126-9003. Available at: <https://myjms.mohe.gov.my/index.php/dismath/article/view/23137>. Date accessed: 26 july 2024.
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