In recent years, fiber optic sensors are widely used in structural health monitoring due to their high-spatial resolution distributed measurements. However, strain transfer through protective coatings of the sensors can distort measurements, especially in high strain gradients. To correct this, mathematical models of strain transfer have been developed and validated through numerical simulations and experiments. Recovering the actual strain profile involves inverting these models, particularly a 1D second-order differential equation derived from a 3D model. This equation, subject to boundary conditions, must be solved repeatedly for efficient numerical inversion. Given the high sampling frequencies of fiber optic sensors, fast algorithms are crucial for real-time applications such as vibration analysis. This paper proposes an efficient method to solve the 1D strain transfer equation and its inverse problem. By enabling rapid post-processing of strain measurements, this approach aims to enhance the application of fiber optic sensors in vibration analysis and structural health monitoring.