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The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other nonreversible partial differential equations, it is useful for often troublesome advection terms. The error estimate is used to correct the data before advection raising the method to second order accuracy, even though each individual step is only first orderdoi:10.1007/s10915-007-9166-4 fatcat:zwcrvhiq6bax5ju47vfpzf3zwy