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Math · Advanced Math
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b) find matrix A
5. Given a heat equation: au-a2au = 0,0 <x<1, 120 The boundary and initial conditions are u(o,t)-ut) and u(x,0) sin(rx) a. Use the backward-Euler method in time and central finite-difference in space to discretize the above parabolic equation.and find the truncation erro Assume the grid is uniform, Δ k, Δχ sh-1/m , and m +1 is the total number of grid points in space. b. The matrix form can be written as AwFind the matrix A 1+41(sin(1 )), where λ-α(k/h). Show tha The eigenvalues of Aare μ the scheme is A-stable. c. 2m
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