Development Partitioning Intervalwise Block Method for Solving Ordinary Differential Equations
Solving Ordinary Differential Equations (ODEs) by
using Partitioning Block Intervalwise (PBI) technique is our aim in
this paper. The PBI technique is based on Block Adams Method and
Backward Differentiation Formula (BDF). Block Adams Method
only use the simple iteration for solving while BDF requires Newtonlike
iteration involving Jacobian matrix of ODEs which consumes a
considerable amount of computational effort. Therefore, PBI is
developed in order to reduce the cost of iteration within acceptable
maximum error
[1] D.S. Watkins, R.W. Hansonsmith (1983). The Numerical
Solution of Separably Stiff System by Precise Partitioning, ACM
Trans Math Software 9. 293-301.
[2] G. Hall, M.B. Suleiman (1985). A single Code for the Solution of
Stiff and Nonstiff ODEs, SIAM J. Stat. Comput. 6(3) 684-697.
[3] K.I. Othman, Z.B. Ibrahim, M. Suleiman, Z. Majid(2007).
Automatic Intervalwise Block Partitioning using Adams type
Method and Backward Differentiation Formula for Solving ODEs,
Applied Maths and Comput 188. 1642-1646.
[4] M.B. Suleiman, S. Baok (1992). Using Nonconvergence of
Iteration to Partitions ODEs, Appl. Math. Comput 49. 111-139.
[5] W.H. Enright, M.S. Kamel (1979), Automatic Partitioning of Stiff
System and Exploiting the Resulting Structure, ACM Trans. Math.
Sofware 5 (4) 374-385.
[6] Z. Majid (2003). Parallel Block Methods For Solving Ordinary
Differential Equations, PhD thesis, University Putra Malaysia.
[1] D.S. Watkins, R.W. Hansonsmith (1983). The Numerical
Solution of Separably Stiff System by Precise Partitioning, ACM
Trans Math Software 9. 293-301.
[2] G. Hall, M.B. Suleiman (1985). A single Code for the Solution of
Stiff and Nonstiff ODEs, SIAM J. Stat. Comput. 6(3) 684-697.
[3] K.I. Othman, Z.B. Ibrahim, M. Suleiman, Z. Majid(2007).
Automatic Intervalwise Block Partitioning using Adams type
Method and Backward Differentiation Formula for Solving ODEs,
Applied Maths and Comput 188. 1642-1646.
[4] M.B. Suleiman, S. Baok (1992). Using Nonconvergence of
Iteration to Partitions ODEs, Appl. Math. Comput 49. 111-139.
[5] W.H. Enright, M.S. Kamel (1979), Automatic Partitioning of Stiff
System and Exploiting the Resulting Structure, ACM Trans. Math.
Sofware 5 (4) 374-385.
[6] Z. Majid (2003). Parallel Block Methods For Solving Ordinary
Differential Equations, PhD thesis, University Putra Malaysia.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:60615", author = "K.H.Khairul Anuar and K.I.Othman and F.Ishak and Z.B.Ibrahim and Z.Majid", title = "Development Partitioning Intervalwise Block Method for Solving Ordinary Differential Equations", abstract = "Solving Ordinary Differential Equations (ODEs) by
using Partitioning Block Intervalwise (PBI) technique is our aim in
this paper. The PBI technique is based on Block Adams Method and
Backward Differentiation Formula (BDF). Block Adams Method
only use the simple iteration for solving while BDF requires Newtonlike
iteration involving Jacobian matrix of ODEs which consumes a
considerable amount of computational effort. Therefore, PBI is
developed in order to reduce the cost of iteration within acceptable
maximum error", keywords = "Adam Block Method, BDF, Ordinary Differential
Equations, Partitioning Block Intervalwise", volume = "5", number = "10", pages = "1634-3", }