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Table 1 Table 1

From: Hierarchies of Difference Boundary Value Problems

 

Original BVP: (1.1) with bc's

Trans. BVP: (2.2) with bc's

No. of evals of Trans. BVP

1

(3.1) with and (3.76)

(3.14) and (3.77)

 

does not obey (3.1) or (3.76)

 

That is, one extra eval

2

(3.1) with and (3.76)

(3.15) and (3.77)

 

does not obey (3.1) or (3.76)

 

That is, one extra eval

3

(3.50) and (3.76)

(3.51) and (3.77)

 

does not obey (3.50) or (3.76)

 

That is, one extra eval

4

(3.1) with and (3.76)

(3.16) and (3.77)

 

obeys (3.1) but not (3.76)

 

That is, same number of evals

5

(3.1) with and (3.76)

(3.17) and (3.77)

 

obeys (3.1) but not (3.76)

 

That is, same number of evals

6

(3.50) and (3.76)

(3.52) and (3.77)

 

obeys (3.50) but not (3.76)

 

That is, same number of evals

7

(3.1) with and (3.76)

(3.14) and (3.78)

 

obeys (3.76) but not (3.1)

 

That is, same number of evals

8

(3.1) with and (3.76)

(3.15) and (3.78)

 

obeys (3.76) but not (3.1)

 

That is, same number of evals

9

(3.50) and (3.76)

(3.51) and (3.78)

 

obeys (3.76) but not (3.1)

 

That is, same number of evals

10

(3.1) with and (3.76)

(3.16) and (3.78)

 

obeys both (3.1) and (3.76)

 

That is, one less eval

11

(3.1) with and (3.76)

(3.17) and (3.78)

 

obeys both (3.1) and (3.76)

 

That is, one less eval

12

(3.50) and (3.76)

(3.52) and (3.78)

 

obeys both (3.50) and (3.76)

 

That is, one less eval