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插值法在含参变量积分中的应用

祝楚恒   

  • 出版日期:1981-03-20 发布日期:1981-03-20

祝楚恒. 插值法在含参变量积分中的应用[J]. 数值计算与计算机应用, 1981, 2(3): 156-162.

APPLICATION OF INTERPOLATION FOR DEFINITE INTEGRAL WITH PARAMETERS

  1. Zhu Chu-heng
  • Online:1981-03-20 Published:1981-03-20
1.问题的提出.在实际计算中,常常需要求下述含有参变量的一维、二维积分. Ⅰ.一维积分 J(γ_1,γ_2,…,γ_n)=∫_(τ_1(γ_1,γ_2…,γ_n))~(τ_2(γ_1,γ_2…,γ_n))F(x)dx, (1.1)其中γ_1,γ_2,…,γ_n为n个实参变量,(γ_1,γ_2,…,γ_n)∈G,而G为n维有界集;F(x)在相应的积分区间上是可积的. Ⅱ.二维积分
In this paper, the following definite integrals:andare considered, where r_1, r_2,…, r_n and α_1, α_2…, α_n, λ are parameters, and the in-tegrated region is defined by the following relations:ψ_1(α_1, α_2, …,α_n) ≤ x ≤ψ_2(α_1, α_2,…, α_n),ψ_1(α_1, α_2,…, α_n, x) ≤ y ≤ψ_2(α_1, α_2,…, α_n,x),where (x, y)∈. A numerical method of computation for definite integral J(r_1,r_2,…,r_n) and I(α_1,α_2,…,α_n; λ) is introduced. The author makes use of the interpolation and numericalmethod of ordinary differential equation as basic idea to compute J (r_1,r_2,…, r_n) andI(α_1, α_2,…, α_n; λ).
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