Abstract
AbstractBy using the splitting‐up technique and cubic spline method, numerical solutions of Burgers' equation ut = uxx + ϵuux, 0 < x < 1, t > 0 and u(x, 0) known, are obtained constructively by taking either of the two pairs of the semi‐linear boundary conditions: (i) u(0, t) = 0, ux(1, t) = aup(1, t), t > 0; (ii) u(1, t) = 0, ux(0, t), = ‐ aup(0, t), where 0 < p < ∞. The stability analysis of the proposed method is discussed.
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