Research Article

Bernstein-Polynomials-Based Highly Accurate Methods for One-Dimensional Interface Problems

Table 4

Convergence analysis of Example 4.1 by Bernstein collocation method ( 𝛽 1 = 1 0 , 𝛽 2 = 1 0 0 ).

𝑁
Equidistant collocation pointsC-G-L collocation points
Cond 𝑢 𝑈 𝐿 2 𝑢 𝑈 𝐻 1 Cond 𝑢 𝑈 𝐿 2 𝑢 𝑈 𝐻 1

4 2 . 4 1 8 6 𝑒 + 0 0 2 1 . 3 4 1 6 𝑒 0 0 5 1 . 8 1 4 5 𝑒 0 0 5 2 . 7 6 0 9 𝑒 + 0 0 2 3 . 7 0 6 5 𝑒 0 0 6 6 . 8 2 3 4 𝑒 0 0 6
6 4 . 6 7 2 0 𝑒 + 0 0 2 1 . 4 3 5 0 𝑒 0 0 8 1 . 9 5 7 5 𝑒 0 0 8 6 . 8 3 7 8 𝑒 + 0 0 2 1 . 5 6 9 2 𝑒 0 0 9 3 . 5 1 3 3 𝑒 0 0 9
8 8 . 0 7 8 5 𝑒 + 0 0 2 9 . 1 0 9 3 𝑒 0 1 2 1 . 2 3 9 0 𝑒 0 1 1 1 . 4 5 1 6 𝑒 + 0 0 3 4 . 1 6 0 1 𝑒 0 1 3 1 . 0 4 5 2 𝑒 0 1 2
10 1 . 8 8 0 3 𝑒 + 0 0 3 1 . 1 0 7 6 𝑒 0 1 4 1 . 3 9 5 3 𝑒 0 1 4 2 . 6 8 7 2 𝑒 + 0 0 3 1 . 3 9 1 2 𝑒 0 1 5 1 . 9 2 1 1 𝑒 0 1 5
12 9 . 7 2 5 3 𝑒 + 0 0 3 2 . 9 2 5 5 𝑒 0 1 4 3 . 5 6 2 2 𝑒 0 1 4 4 . 4 8 8 2 𝑒 + 0 0 3 1 . 5 7 4 6 𝑒 0 1 5 2 . 4 9 9 4 𝑒 0 1 5