A direct numerical procedure for the Cauchy problem for the heat equation |
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| Authors: | JR Cannon Richard E Ewing |
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| Institution: | Department of Mathematics, University of Texas at Austin, Austin, Texas 78712 USA;Department of Mathematics, Oakland University, Rochester, Michigan 48063 USA |
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| Abstract: | For the Cauchy problem, ut = uxx, 0 < x < 1, 0 < t ? T, u(0, t) = f(t), 0 < t ? T, ux(0, t) = g(t), 0 < t ? T, a direct numerical procedure involving the elementary solution of υt = υxx, 0 < x, 0 < t ? T, υx(0, t) = g(t), 0 < t ? T, υ(x, 0) = 0, 0 < x and a Taylor's series computed from f(t) ? υ(0, t) is studied. Continuous dependence better than any power of logarithmic is obtained. Some numerical results are presented. |
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