This paper presents an adaptive block time-stepping algorithm designed for the numerical integration of first-order stiff oscillatory problems, which typically involve multiple time scales and stringent stability conditions. The proposed method integrates a block formulation enabling the simultaneous evaluation of several solution points with an adaptive step size mechanism to effectively regulate local truncation errors. A predictor-corrector strategy is employed, where an explicit predictor generates initial estimates, and an implicit block corrector enhances stability for stiff systems. The resulting nonlinear equations are resolved using Newton's iterative method. The scheme is proven to... More >