* Stop 6: York and Vallette -- Approximate
boarding time is 25 and 55 minutes after the hour.
Substituting the approximate
unknown vector nodes [H.sup.n.sub.i,M+1], [U.sup.n.sub.i,M+1], and [V.sup.n.sub.i,M+1] of the upper boundary into (8), (10), and (12), respectively,
Equation (3) is approximately invariant under the approximate
transformation group (2) with the generator
Realizing the importance of obtaining accurately, a few studies [26, 28, 30] considered Mx and other absorption parameters as unknown to be determined from the approximate
solutions for longer and shorter times, given in Eqs.
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Use the similarity variables (8) to get the approximate
solution of original IBVP (6)-(7).
We assume that the approximate
periodic solutions of (7) and (8) can be expressed as
It is convenient in both theory and practice to approximate
the complex integral and then obtain trigonometric integrals from the real and imaginary parts of the result,
However, if the approximate
query request is always sent to the centric storage node directly, it may bring in great message complexity.
Usually, for problems of the type (1,2), it is difficult, and sometimes impossible to find an exact solution, hence a numerical solution or an approximate
analytical solution must be found, by using various methods such as : methods based on Taylor polynomials and Chebyshev polynomials (Chena et al., 2005), homotopy methods (He, 2003), collocation-type methods (Gotovac et al., 2009).
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