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Contents >> Applied Mathematics >> Numerical Methods >> Interpolation of Functions >> Example

Interpolation of functions - Example

Example [1]

The table of values of full elliptic integral

is given; find  К(78º 30’).

Values of full elliptic integral K(α)

α

K(α)

ΔK

Δ2K

Δ3K

Δ4K

Δ5K

Δ6K

75º

2.76806

 

 

 

 

 

 

 

 

6461

 

 

 

 

 

76º

2.83267

 

528

 

 

 

 

 

 

6989

 

84

 

 

 

77º

2.90256

 

612

 

19

 

 

 

 

7601

 

103

 

13

 

78º

2.97857

 

715

   

32

 

– 5

 

 

8316

 

135

 

8

 

79º

3.06173

 

850

 

40

 

18

 

 

9166

 

175

 

26

 

80º

3.15339

 

1025

 

66

 

– 1

 

 

10191

 

241

 

25

 

81º

3.25530

 

1266

 

91

 

43

 

 

11457

 

332

 

68

 

82º

3.36987

 

1598

 

159

 

 

 

 

13055

 

491

 

 

 

83º

3.50042

 

2089

 

 

 

 

 

 

15144

 

 

 

 

 

84º

3.65186

 

 

 

 

 

 

 

S o l u t i o n .   According to data of the table it is accepted х0 = 78º ;  h =1º ;  х = 78º 30’, from here q = 0.5. Being limited to differences of the fifth order, from Stirling’s interpolation formula we have:

 

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