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Theory and Modern Applications

Table 4 Results for Example  3

From: Numerical solution of Volterra partial integro-differential equations based on sinc-collocation method

N

\(\boldsymbol{\Delta t = 10^{-5}}\)

\(\boldsymbol{\Delta t =10^{-6}}\)

\(\boldsymbol{\Delta t =10^{-7}}\)

SMLP

SMTR

SMLP

SMTR

SMLP

SMTR

8

2.75 × 10−3

8.52 × 10−4

1.05 × 10−3

8.28 × 10−4

3.57 × 10−6

9.81 × 10−7

2.83 × 10−3

8.94 × 10−4

2.58 × 10−3

8.41 × 10−4

1.65 × 10−4

7.34 × 10−6

2.87 × 10−3

9.86 × 10−4

2.61 × 10−3

9.73 × 10−4

4.35 × 10−4

6.52 × 10−5

2.88 × 10−3

9.71 × 10−3

2.61 × 10−3

8.84 × 10−3

6.13 × 10−4

1.41 × 10−4

16

2.75 × 10−4

7.32 × 10−5

2.63 × 10−4

7.28 × 10−5

9.00 × 10−5

6.87 × 10−7

2.92 × 10−4

6.54 × 10−5

2.66 × 10−4

1.79 × 10−5

2.56 × 10−4

5.62 × 10−6

6.45 × 10−4

8.30 × 10−5

2.67 × 10−4

5.48 × 10−5

2.61 × 10−4

6.42 × 10−6

1.08 × 10−3

9.24 × 10−5

2.67 × 10−4

6.74 × 10−5

2.61 × 10−4

7.83 × 10−6

32

5.28 × 10−5

9.12 × 10−6

9.81 × 10−6

5.41 × 10−6

8.66 × 10−6

1.19 × 10−7

2.92 × 10−4

4.37 × 10−5

9.81 × 10−6

4.09 × 10−6

8.66 × 10−6

4.72 × 10−7

6.45 × 10−4

5.83 × 10−5

2.04 × 10−5

6.49 × 10−6

8.66 × 10−6

7.28 × 10−7

1.08 × 10−3

7.34 × 10−5

3.43 × 10−5

8.51 × 10−6

8.66 × 10−6

8.63 × 10−7

64

5.28 × 10−5

3.41 × 10−6

1.67 × 10−6

9.86 × 10−7

6.11 × 10−8

7.53 × 10−8

2.92 × 10−4

1.92 × 10−5

9.24 × 10−6

5.17 × 10−6

2.28 × 10−7

8.91 × 10−8

6.45 × 10−4

4.56 × 10−5

2.04 × 10−5

6.84 × 10−6

6.45 × 10−7

9.52 × 10−8

1.08 × 10−3

5.37 × 10−5

3.43 × 10−5

7.13 × 10−6

9.44 × 10−7

1.54 × 10−7