边值问题导论

Ordinary Differential Equations and Boundary Value Problems Pub Date : 2018-09-18 DOI:10.1142/9789813274037_0001

D. Gleich

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摘要

1 # 我们使用网格表示 [0, 1] 上的函数 u(x) 2 # 因此，我们将 [0, 1] 分成 N + 1 个增量，每个增量为 1/N。3 4 N = 10 5 xgrid = collect(0:1/N:1) 6 7 # 这意味着 u 是一个有 n = N+1 个元素的向量，8 # 但其中两个元素固定为 alpha 和 beta。9 10 n = length(xgrid) 11 12 example_u = zeros(n); 13 example_u[1] = 1 # 假设 alpha = 1 14 example_u[end] = 1/2 # 假设 beta = 1/2 15 16 example_u[2:end-1] = 1.06-1*(xgrid[2:end-1]-0.25).^2; 17 18 plot(xgrid, example_u)

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Introduction to Boundary Value Problems

1 # We use a grid representation of the function u(x) on [0, 1] 2 # so we divide [0, 1] up into N + 1 increments of 1/N each. 3 4 N = 10 5 xgrid = collect(0:1/N:1) 6 7 # This means that u is a vector with n = N+1 elements, 8 # but two of them are fixed at alpha and beta. 9 10 n = length(xgrid) 11 12 example_u = zeros(n); 13 example_u[1] = 1 # suppose alpha = 1 14 example_u[end] = 1/2 # suppose beta = 1/2 15 16 example_u[2:end-1] = 1.06-1*(xgrid[2:end-1]-0.25).^2; 17 18 plot(xgrid, example_u)

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Ordinary Differential Equations and Boundary Value Problems

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