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Theory and Modern Applications

Table 4 Numerical results of CFDS-PIM (\(\tau=1\times10^{-4}\)) and Ref. [34] (\(\tau=1\times10^{-6}\)) at \(t=1\) for case 3 of Example 1

From: A new high-order compact finite difference scheme based on precise integration method for the numerical simulation of parabolic equations

 

h

0.2

0.1

0.05

Taylor

Max(error)

6.056 × 10−8

1.218 × 10−9

6.821 × 10−12

CPU (s)

0.025

0.027

0.030

Padé

Max(error)

6.056 × 10−8

1.217 × 10−9

3.341 × 10−12

CPU (s)

0.030

0.031

0.031

Ref. [34]

Max(error)

4.770 × 10−6

7.714 × 10−9

1.882 × 10−11

CPU (s)