an effective adaptive algorithm to calculate the steady-state response of circuits is developed. this algorithm offers a powerful alternative to traditional steady-state simulation techniques, such as the shooting method or harmonic balance (hb). a favourable feature of the algorithm is that it obtains the unknown circuit solutions by using adaptive basis functions (abf). the circuit equations are formulated by transformation matrices. one of the contributions of this thesis is to use the least squares method instead of galerkin method to solve ordinary differential equations with abf. another contribution is that the proposed algorithm uses different grid resolutions to represent each state variable simultaneously. the position of the grid points for each state variable is adaptively controlled by an algorithm that attempts to minimize artifact oscillations in the solutions. the algorithm is demonstrated by simulating two circuits and comparing the results with spice and aplac.