Worked on the gridap/Gridap.jl repository to enhance the reliability of ODE solvers used in scientific computing applications. Focused on improving the numerical correctness and stability of the ODE solving path by addressing a cache indexing issue within RungeKuttaIMEX.jl. The solution involved refining how cache updates occur during integration, thereby reducing the risk of inaccuracies for users modeling dynamic systems. Utilized Julia programming and applied knowledge of numerical methods to implement and validate the fix. This targeted engineering effort contributed to more robust solver behavior, supporting accurate simulations in environments that rely on precise numerical computations and scientific workflows.