2025-04-01https://repository.covenantuniversity.edu.ng/handle/123456789/41195This paper intends to investigate the use of a dilated trigonometrically equipped algorithm to compute periodic vibrations in block Milne’s implementation. The block-Milne implementation is established by developing a block variablestep-size predictor-corrector method of Adam’s family using a dilated trigonometrically equipped algorithm. The execution is carried out using a block variable-step-size predictor-corrector method. This system has significant advantages that include the varying step-size and finding out the convergence-criteria and error control. Convergence-criteria and operational mode are discussed to showcase the accuracy and effectuality of the proposed approach.application/pdfQ Science (General), QA MathematicsArticle