LAUSR

For the later development, the following denotations are (iteratively) defined by   A10(η[3]) = η3−η1 η2−η1 , A11(η[5]) = η5(η4−η1) (η2−η1)(η3−η1) , A1i(η[3i+1]) = ∏3i+1 j=2i+2 ηj(η2i+1−η1) ∏i j=1(η2j−η2j−1)(η3−η1) , A20(η[3]) = η3 η2−η1 , A21(η[5]) = −η4η5 (η2−η1)(η3−η1) , A2i(η[3i+1]) = − ∏3i+1 j=2i+1 ηj ∏i j=1(η2j−η2j−1)(η3−η1) , A30(η[2]) = 1 η2−η1 , A31(η[4]) = η4 (η2−η1)(η3−η1) , A3i(η[3i]) = ∏3i j=2i+1 ηj ∏i j=1(η2j−η2j−1)(η3−η1) , A40(η[2]) = −η1 η2−η1 , A41(η[4]) = −η1η4 (η2−η1)(η3−η1) , A4i(η[3i]) = − ∏3i j=2i+1 ηjη1 ∏i j=1(η2j−η2j−1)(η3−η1) , i = 1, . . . , N − 1, Φ0(t, η1) = e −η1t,Φ1(t, η[2]) = e −η1t − e−η2t, Φi(t, η[i+1]) = Φi−1(t,[η1,η T [3,i+1]] ) η3−η1 − Φi−1(t,[η2,η T [3,i+1]] ) η3−η2 , i = 2, . . . , N − 1, (A1)