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Table 5 Results for \(\|u^{n}-U^{n}_{h}\|_{1}\) (\(h=\frac{1}{160}\), \(\tau=kh\))

From: A new approach to convergence analysis of linearized finite element method for nonlinear hyperbolic equation

t

k = 1

k = 5

k = 10

k = 20

k = 40

0.25

2.396051 × 10−3

2.509776 × 10−3

2.868899 × 10−3

4.142662 × 10−3

7.852834 × 10−3

0.50

3.093389 × 10−3

3.652433 × 10−3

5.078443 × 10−3

8.767703 × 10−3

1.632563 × 10−2

0.75

4.009582 × 10−3

5.496080 × 10−3

8.725847 × 10−3

1.598647 × 10−2

2.828099 × 10−2

1.00

5.216721 × 10−3

8.300234 × 10−3

1.426017 × 10−2

2.670072 × 10−2

4.519938 × 10−2