Table 8 Absolute errors for \(\mathfrak{h}(t)=t\) and \(\sigma (x, t)=0.8+0.005\cos (xt) \sin (x)\) at equally spaced points \((x_{j}, t_{j})\) for Example 6.4

(0.0, 0.0)

0.0000

0.0000

0.0000

0.00

(0.1, 0.1)

4.6564 × 10⁻⁷

1.3174 × 10⁻⁸

9.1996 × 10⁻¹⁰

6.71 × 10⁻⁸

(0.2, 0.2)

2.1675 × 10⁻⁶

1.9799 × 10⁻⁸

2.7846 × 10⁻⁹

5.56 × 10⁻⁸

(0.3, 0.3)

9.2951 × 10⁻⁷

1.6713 × 10⁻⁷

8.3848 × 10⁻⁹

3.44 × 10⁻⁸

(0.4, 0.4)

1.7223 × 10⁻⁵

5.4651 × 10⁻⁷

2.1337 × 10⁻⁸

1.00 × 10⁻⁷

(0.5, 0.5)

4.9474 × 10⁻⁵

7.8736 × 10⁻⁷

1.0666 × 10⁻⁷

1.75 × 10⁻⁷

(0.6, 0.6)

9.0602 × 10⁻⁵

5.2274 × 10⁻⁷

2.1247 × 10⁻⁷

1.48 × 10⁻⁷

(0.7, 0.7)

1.2583 × 10⁻⁴

2.3837 × 10⁻⁷

2.7283 × 10⁻⁷

1.05 × 10⁻⁷

(0.8, 0.8)

1.4134 × 10⁻⁴

9.3766 × 10⁻⁷

2.6298 × 10⁻⁷

3.36 × 10⁻⁷

(0.9, 0.9)

1.3712 × 10⁻⁴

8.3631 × 10⁻⁷

2.5434 × 10⁻⁷

7.37 × 10⁻⁷

(1.0, 1.0)

1.3951 × 10⁻⁴

4.6873 × 10⁻⁷

2.9456 × 10⁻⁷

8.58 × 10⁻⁷