A Finite Element Collocation Method for Quasilinear Parabolic Equations
نویسنده
چکیده
Let the parabolic problem cix, t, u)ut = aix, t, u)uxx + bix, t, u, ux), 0 < x < 1, 0 < / á T, uix, 0) = fix), w(0, t) = gli), ií(1, t) = giit), be solved approximately by the continuous-time collocation process based on having the differential equation satisfied at Gaussian points £,,i and £;,2 in subintervals (x,-_i, x¡) for a function l/:[0, T] —» 3C3, the class of Hermite piecewise-cubic polynomial functions with knots 0 = x0 < Xi < ■ ■ ■ < xn = 1. It is shown that u — U = 0(A4) uniformly in x and t, where h = max(x, — x,-_i).
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تاریخ انتشار 2010