Table 2: (a) The errors of the numerical solutions of (2.22) by methods {(7.1), (3.10)}, (b) The CPU times (in second) of methods (3.7)–(3.10) for (2.23) and (c) The CPU times (in second) of methods {(7.1), (3.10)} for (2.23).
(a)

( Δ 𝑣 , ) Gauss Radau IA Radau IIA Lobatto IIIC

( 𝜋 / 3 0 , 3 / 1 6 ) 9 . 0 1 9 3 𝑒 0 0 6 3 . 7 2 7 3 𝑒 0 0 4 3 . 8 9 6 6 𝑒 0 0 4 1 . 4 0 8 3 𝑒 0 0 2
( 𝜋 / 6 0 , 3 / 3 2 ) 5 . 6 7 3 9 𝑒 0 0 7 4 . 6 4 9 1 𝑒 0 0 5 4 . 9 5 5 8 𝑒 0 0 5 3 . 5 4 5 3 𝑒 0 0 3
( 𝜋 / 1 2 0 , 3 / 6 4 ) 3 . 5 5 3 4 𝑒 0 0 8 5 . 7 9 3 3 𝑒 0 0 6 6 . 2 3 6 0 𝑒 0 0 6 8 . 8 9 1 2 𝑒 0 0 4
( 𝜋 / 2 4 0 , 3 / 1 2 8 ) 2 . 2 2 1 7 𝑒 0 0 9 7 . 2 2 8 4 𝑒 0 0 7 7 . 8 1 8 6 𝑒 0 0 7 2 . 2 2 6 1 𝑒 0 0 4

(b)

( Δ 𝑣 , ) Gauss Radau IA Radau IIA Lobatto IIIC

( 𝜋 / 3 0 , 3 / 1 6 ) 7 . 0 7 8 0 𝑒 + 0 0 0 6 . 8 7 5 0 𝑒 + 0 0 0 6 . 9 0 6 0 𝑒 + 0 0 0 6 . 9 3 8 0 𝑒 + 0 0 0
( 𝜋 / 6 0 , 3 / 3 2 ) 4 . 4 4 6 8 𝑒 + 0 0 1 4 . 4 5 0 0 𝑒 + 0 0 1 4 . 4 7 6 6 𝑒 + 0 0 1 4 . 5 1 7 2 𝑒 + 0 0 1
( 𝜋 / 1 2 0 , 3 / 6 4 ) 3 . 3 0 3 9 𝑒 + 0 0 2 3 . 3 1 5 6 𝑒 + 0 0 2 3 . 3 2 8 1 𝑒 + 0 0 2 3 . 3 2 6 4 𝑒 + 0 0 2
( 𝜋 / 2 4 0 , 3 / 1 2 8 ) 2 . 7 1 1 7 𝑒 + 0 0 3 2 . 7 0 4 2 𝑒 + 0 0 3 2 . 7 1 0 9 𝑒 + 0 0 3 2 . 7 2 9 1 𝑒 + 0 0 3

(c)

( Δ 𝑣 , ) Gauss Radau IA Radau IIA Lobatto IIIC

( 𝜋 / 3 0 , 3 / 1 6 ) 4 . 2 1 8 0 𝑒 + 0 0 0 4 . 2 3 5 0 𝑒 + 0 0 0 4 . 2 6 5 0 𝑒 + 0 0 0 4 . 2 8 2 0 𝑒 + 0 0 0
( 𝜋 / 6 0 , 3 / 3 2 ) 3 . 0 9 5 3 𝑒 + 0 0 1 3 . 0 2 3 4 𝑒 + 0 0 1 3 . 1 0 3 1 𝑒 + 0 0 1 3 . 1 1 2 5 𝑒 + 0 0 1
( 𝜋 / 1 2 0 , 3 / 6 4 ) 2 . 7 0 5 5 𝑒 + 0 0 2 2 . 8 4 0 0 𝑒 + 0 0 2 2 . 7 2 1 3 𝑒 + 0 0 2 2 . 7 1 0 5 𝑒 + 0 0 2
( 𝜋 / 2 4 0 , 3 / 1 2 8 ) 2 . 7 8 2 1 𝑒 + 0 0 3 2 . 8 1 6 4 𝑒 + 0 0 3 2 . 7 9 5 0 𝑒 + 0 0 3 2 . 8 0 0 6 𝑒 + 0 0 3