Adaptive Predictor-Corrector Schemes for a Class of Pantograph-Type Delay Differential Equations

Abstract

This study highlights the new adaptive predictor-corrector scheme which is combined with the Gauss’ forward interpolation strategy to handle the properties of time delays in a single delay pantograph. This scheme provides an entirely new perspective on accurate and efficient approaches since the scheme considered a technique that employs both odd and even differences under the central interpolation approximation which can be adapted in the particular pantograph delays. To guarantee that the time delay approximation yields a high degree of accuracy in comparison to alternative methods, a thorough analysis is given to the interpolation node selection. Aside from that, the convergence and stability analysis which includes the order, error constant, zero-stability and consistency of the suggested approach are examined. Numerical problems are provided to show the practical advantages of the suggested algorithms and to compare with the exact results. Based on the findings, it can be concluded that the numerical method of the adaptive predictor-corrector scheme, which was used to solve the single pantograph delay, is reliable with high error accuracy. The novelty of the method lies in its adaptive multistep structure combined with Gauss’s interpolation, which enhances precision and improves the handling of time-delay terms.