Diagonally multistep block method for solving Volterra integro-differential equation with delay

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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