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Theory and Modern Applications

Table 2 \(L_{2}\) and \(L_{\infty }\) norms for Problem 1 when \(\lambda =0.1\) and \(\nu =-10\)

From: Application of new quintic polynomial B-spline approximation for numerical investigation of Kuramoto–Sivashinsky equation

t

QnBS–DQM [6]

Proposed method

\(L_{2}\)

\(L_{\infty }\)

\(L_{2}\)

\(L_{\infty }\)

0.1

8.50 × 10−3

8.59 × 10−3

1.74 × 10−4

1.17 × 10−4

0.3

1.18 × 10−2

9.52 × 10−3

3.36 × 10−4

2.12 × 10−4

0.5

1.44 × 10−2

1.00 × 10−2

4.72 × 10−4

2.83 × 10−4

0.7

1.69 × 10−2

1.04 × 10−2

5.83 × 10−4

3.35 × 10−4

1.0

1.92 × 10−2

1.19 × 10−2

7.14 × 10−4

3.87 × 10−4