A 14-Order Hybrid Block Method in Variable Step-Size Mode for Solving Second-Order Initial Value Problems

Algorithm 1

Variable step-size mode implementation.

Require:(integration interval),(initial values),

1. Set, Let

2. Let, Let.

3. Solve Equations (12)–(17), (19)–(24) to get

4. Let.

5. Let

6. Let

7. If

8. then go to 3

9. else

10. go to 11 then

11. Obtain

12. end if else

13. Solve Equation (51) to get

14. Obtain LE using

15. ifthen

16. the result is accepted and the next step-size is

   taken as

17. else

18. the result is rejected.

19. go to 15 with the new step-size

20. 

21. whereis the order of the LOF and,

   which serves as a safety factor to avoid failure

   steps

22. end if else

23. End