This paper is concerned with the challenging and timely problem of channel estimation for orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency selective and very rapidly time varying channels. In OFDM systems operating over rapidly time-varying channels, the orthogonality between subcarriers is destroyed leading to inter-carrier interference (ICI) and resulting in an irreducible error floor. The band-limited, discrete cosine serial expansion of low-dimensionality is employed to represent the time-varying channel. In this way, the resulting reduced dimensional channel coefficients are estimated iteratively with tractable complexity and independently of the channel statistics. The algorithm is based on the expectation maximization-maximum a posteriori probability (EM-MAP) technique leading to a receiver structure that also yields the equalized output using the channel estimates. The pilot symbols are employed to estimate the initial coefficients effectively and unknown data symbols are averaged out in the algorithm in a non-data-aided fashion. It is shown that the computational complexity of the proposed algorithm to estimate the channel coefficients and to generate the equalized output as a by-product is ∼ O(N) per detected symbol, N being the number of OFDM subcarriers. Computational complexity as well as computer simulations carried out for the systems described in WiMAX and LTE standards indicate that it has significant performance and complexity advantages over existing suboptimal channel estimation and equalization algorithms proposed earlier in the literature.