Memristive crossbar arrays are a key technology for analog in-memory computing in AI accelerators and neuromorphic systems. The inherent device nonlinearities are advantageous, suppressing sneak-path currents in selector-less (1R) arrays, enabling 3D back-end-of-line integration, and ensuring read stability against the voltage-time dilemma. However, these same properties, combined with device variability, IR drop, and parasitic effects, severely challenge precise programming. Conventional amplitude-modulated write-verify algorithms are consequently slow, energy-intensive, and limited by write endurance. Here, a time-modulated write algorithm is introduced, specifically designed for analog-switching 1R crossbars. It employs a single programming voltage, varying only the write pulse duration. The algorithm leverages a compact model to estimate an initial optimal write time, which is then refined by a dynamic gain mechanism that rapidly compensates for deviations arising from non-ideal effects. The method's performance is validated through SPICE simulations of a physics-based (Formula presented.) / (Formula presented.) model across various crossbar sizes and V/2, V/3 and floating biasing schemes. The results demonstrate that the time-modulated approach significantly reduces write iterations and total programming time, while simultaneously lowering energy consumption and improving final conductance accuracy. This proposed algorithm enables faster, more energy-efficient weight updates and restoration in memristive neural network accelerators.