Table 1 A comparison of the approximate analytic solution with the matrix-vector barycentric polynomials \(u_{n} ( x_{i} )\) for \(n = 2,3,5,15,20\) at \(x_{i} = - 1:0.2:1\)

−1

1.6425

1.6388

1.6345

1.6403

1.6397

1.6397

−0.8

1.7312

1.7731

1.7423

1.7344

1.7307

1.7307

−0.6

1.8099

1.8776

1.8262

1.8119

1.8097

1.8097

−0.4

1.8698

1.9522

1.8861

1.8696

1.8696

1.8696

−0.2

1.9068

1.997

1.922

1.9052

1.9066

1.9066

0

1.9192

2.0119

1.934

1.9172

1.919

1.919

0.2

1.9068

1.997

1.922

1.9052

1.9066

1.9066

0.4

1.8698

1.9522

1.8861

1.8696

1.8696

1.8696

0.6

1.8099

1.8776

1.8262

1.8119

1.8097

1.8097

0.8

1.7312

1.7731

1.7423

1.7344

1.7307

1.7307

1

1.642

1.6388

1.6345

1.6403

1.6397

1.6397