𝑃-Stable Higher Derivative Methods with Minimal Phase-Lag for Solving Second Order Differential Equations

Table 1

Methods

𝑆

𝛽10

𝛽11

𝑎0

𝑎1

𝑎2

𝑎−1

𝑎−2

𝑏0

𝑏1

𝐵2

𝑏−1

𝑏−2

Explicit

−1

2

−1

0

−1/2

−1/4

7/2

−7/4

0

1

2

−1

−2

Implicit

3

1/2

1/2

0

3/2

3/4

−5/2

5/4

0

1

2

−1

−2

Explicit

5/4

11/32

21/32

0

5/8

5/16

1/8

−1/16

0

1

2

−1

−2

Explicit

3/2

11/32

21/32

0

3/4

3/8

−1/4

1/8

0

1

2

−1

−2

Implicit

2

−2/3

5/3

0

1

1/2

−1

1/2

0

1

2

−1

−2

Implicit

−2

8/3

−5/3

0

−1

−1/2

1

−1/2

0

1

2

−1

−2

Explicit

−3/2

53/32

−21/32

0

−3/4

−3/8

1/4

−1/8

0

1

2

−1

−2

Explicit

−5/4

53/32

−21/32

0

−5/8

−5/16

−1/8

1/16

0

1

2

−1

−2

Implicit

−13

13/12

−1/12

0

−13/2

−13/4

35/2

−35/4

0

1

2

−1

−2

Explicit

1

0

1

0

1/2

1/4

−3/2

3/4

0

1

2

−1

−2