Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model
نویسندگان
چکیده
and Applied Analysis 3 Proof. If we let h s ∑∞ n 1 ans n and substituting into 1.3 , we have α2 ∞ ∑ n 0 n 1 λ − 1 an 1s 2α ∞ ∑ n 1 ( n−1 ∑ i 0 i 1 ( λn−i − 1 )( λ − 1 ) an−iai 1 ) s ∞ ∑ n 2 ( n−2 ∑ i 0 n−i−1 ∑ k 1 i 1 ( λn−k−i − 1 )( λ − 1 )( λ − 1 ) an−k−iakai 1 ) s β ∞ ∑ n 1 ( n−1 ∑ i 0 i 1 ( λn−i − 1 )2 an−iai 1 ) s. 2.3 Comparing coefficients we obtain α2 ( λ0 − 1 ) a1 0, 2.4 α2 n 1 λ − 1 an 1 β n−1 ∑ i 0 i 1 ( λn−i − 1 )2 an−iai 1 − 2α n−1 ∑ i 0 i 1 ( λn−i − 1 )( λ − 1 ) an−iai 1
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