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Four numerical problems consisting of linear ordinary differential equations and trigonometric equations with different step sizes were performed to validate the accuracy of the proposed methods. The numerical results were compared with the least squares method, finite difference method, finite element ...
In particular, it shows that the gradient ∇𝐶̂ (𝜃)∇C^(θ) is smooth, and moreover, each of its entries is a trigonometric polynomial on the 2𝑛2n variables 𝑐𝑗=cos(𝜃𝑗2)cj=cosθj2 and 𝑠𝑗=sin(𝜃𝑗2)sj=sinθj2, for 𝑗=1,…,𝑛j=1,…,n. Thus...
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