Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations
A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at {xn,xn+r} while its second and third derivatives a...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/8510948 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558106367754240 |
|---|---|
| author | Mohammad Alkasassbeh Zurni Omar |
| author_facet | Mohammad Alkasassbeh Zurni Omar |
| author_sort | Mohammad Alkasassbeh |
| collection | DOAJ |
| description | A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at {xn,xn+r} while its second and third derivatives are collocated at all points {xn,xn+r,xn+s,xn+t,xn+1} in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy. |
| format | Article |
| id | doaj-art-752598f1613e46bfab314562457337b9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-752598f1613e46bfab314562457337b92025-02-03T01:33:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422017-01-01201710.1155/2017/85109488510948Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential EquationsMohammad Alkasassbeh0Zurni Omar1Department of Mathematics, School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia, Sintok, MalaysiaDepartment of Mathematics, School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia, Sintok, MalaysiaA new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at {xn,xn+r} while its second and third derivatives are collocated at all points {xn,xn+r,xn+s,xn+t,xn+1} in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy.http://dx.doi.org/10.1155/2017/8510948 |
| spellingShingle | Mohammad Alkasassbeh Zurni Omar Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations Journal of Applied Mathematics |
| title | Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations |
| title_full | Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations |
| title_fullStr | Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations |
| title_full_unstemmed | Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations |
| title_short | Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations |
| title_sort | implicit one step block hybrid third derivative method for the direct solution of initial value problems of second order ordinary differential equations |
| url | http://dx.doi.org/10.1155/2017/8510948 |
| work_keys_str_mv | AT mohammadalkasassbeh implicitonestepblockhybridthirdderivativemethodforthedirectsolutionofinitialvalueproblemsofsecondorderordinarydifferentialequations AT zurniomar implicitonestepblockhybridthirdderivativemethodforthedirectsolutionofinitialvalueproblemsofsecondorderordinarydifferentialequations |