Consider the implicit scheme for heat conduction problem U_s^n + 1 - U_j^n = sig
ID: 2875353 • Letter: C
Question
Consider the implicit scheme for heat conduction problem U_s^n + 1 - U_j^n = sigma/h^2 (U_j + 1^n + 1 - 2 U_j^n + 1 + U_j - 1^n + 1) + S_j^n + 1, 1 lessthanorequalto j lessthanorequalto M - 1, 0 lessthanorequalto n lessthanorequalto N {U_j^0 = u_0 (X_j) U_0^n = 0, U_m^n = 0 Where the truncation error TE_j^n + 1 = 0 (Delta t + h^2), with |TE_j^n + 1| lessthanorequalto (t Delta t + h^2) Use the discrete energy method to show that the implicit scheme is unconditionally stable and convergent with 0 lessthanorequalto j lessthanorequalto M |e_j^n| lessthanorequalto C_0 (Delta t + h^2). Here, C_0 is a constant, Mh = b - a and n Delta t lessthanorequalto T.Explanation / Answer
Solution:
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