Method and system are disclosed for simulating a circuit. The method includes representing a circuit using a matrix that represents a set of linear equations to be solved, identifying a delta matrix, which is a subset of the matrix that changed states from a previous time step to a current time step, computing an update of the delta matrix using a matrix decomposition approach, generating a current state of the matrix using a previous state of the matrix and the update of the delta matrix, and storing the current state of the matrix in a memory device.