1. The document proposes an algorithmic framework for large-scale circuit simulation using exponential integrators. It uses exponential Rosenbrock methods and an invert Krylov subspace approach to efficiently compute the matrix exponential-vector product to solve the circuit equations explicitly without needing Newton-Raphson iterations. 2. The framework was shown to accurately simulate benchmark circuits while achieving speedups over traditional approaches. It can handle large-scale, strongly coupled circuits that traditional methods have difficulty with. 3. Future work includes exploring parallelization opportunities to further accelerate the method using multicore/many-core systems and developing additional tools based on the proposed derivatives-based approach.