(3) Study the truncation error and stability of the following schemes. (A) The explicit scheme for...

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(3) Study the truncation error and stability of the following schemes. (A) The explicit scheme for the heat equation U =14xx, Do is a constant. (Hint: study the 1 stability) (B) The Crank-Nicolson scheme for the heat equation. (Hint: use Fourier transform to obtain the Fourier symbol S(34x)). (C) For the equation U = V Uxx + Ux, (N>o is a constant) consider the following scheme (Crank-Nicolson): n+l - 2 ntl n+ n+l = 1) { U;+1 - 20 ; " + U; -11 ,n+1 - 20% Ax2 n+1 0; +} + 4x Un-U 247 -}. (3) Study the truncation error and stability of the following schemes. (A) The explicit scheme for the heat equation U =14xx, Do is a constant. (Hint: study the 1 stability) (B) The Crank-Nicolson scheme for the heat equation. (Hint: use Fourier transform to obtain the Fourier symbol S(34x)). (C) For the equation U = V Uxx + Ux, (N>o is a constant) consider the following scheme (Crank-Nicolson): n+l - 2 ntl n+ n+l = 1) { U;+1 - 20 ; " + U; -11 ,n+1 - 20% Ax2 n+1 0; +} + 4x Un-U 247 -}.

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A Heat Equation Explicit Scheme The heat equations explicit scheme is provided by 1 2 1 2 1 U n1 j U ... View the full answer