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Theory and Modern Applications

Table 5 Comparisons by the maximum errors to Example 1 for \(h=1/25\) (i.e., \(m-1=24=6K\), \(K=4\))

From: A new parallel algorithm for solving parabolic equations

Methods

r

t = 0.2

t = 0.4

t = 0.6

t = 0.8

Algorithm 1

0.38

1.5929e−4

2.1698e−4

2.6806e−4

3.2777e−4

ASC-N scheme [6]

2.4785e−4

3.7370e−4

4.7785e−4

8.3215e−4

Algorithm 1

0.63

2.2660e−4

3.0852e−4

3.8124e−4

4.6627e−4

ASC-N scheme [6]

2.8997e−4

4.3826e−4

6.5392e−4

9.7553e−4

Algorithm 1

0.94

3.0760e−4

4.1963e−4

5.1826e−4

6.3353e−4

ASC-N scheme [6]

4.5949e−4

6.9190e−4

8.3264e−4

1.5416e−3

Algorithm 1

1.35

3.8737e−4

5.2761e−4

6.5199e−4

7.9740e−4

ASC-N scheme [6]

4.2810e−4

6.4710e−4

9.6552e−4

1.4404e−3

Algorithm 1

1.76

4.6541e−4

6.3397e−4

7.8343e−4

9.5815e−4

ASC-N scheme [6]

 

4.6674e−4

7.0553e−4

1.0527e−3

1.5704e−3