Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems
For solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/6457532 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849399513759875072 |
|---|---|
| author | Alicia Cordero Esther Gómez Juan R. Torregrosa |
| author_facet | Alicia Cordero Esther Gómez Juan R. Torregrosa |
| author_sort | Alicia Cordero |
| collection | DOAJ |
| description | For solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new methods is compared with those of some known ones, obtaining good conclusions, due to the particular structure of the iterative expression of the proposed methods. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and a nonlinear one-dimensional heat conduction equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the presented schemes. |
| format | Article |
| id | doaj-art-9d989657be4f48e79637bbdca9b98d99 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-9d989657be4f48e79637bbdca9b98d992025-08-20T03:38:19ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/64575326457532Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction ProblemsAlicia Cordero0Esther Gómez1Juan R. Torregrosa2Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, SpainUniversitat de València, Valencia, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, SpainFor solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new methods is compared with those of some known ones, obtaining good conclusions, due to the particular structure of the iterative expression of the proposed methods. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and a nonlinear one-dimensional heat conduction equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the presented schemes.http://dx.doi.org/10.1155/2017/6457532 |
| spellingShingle | Alicia Cordero Esther Gómez Juan R. Torregrosa Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems Complexity |
| title | Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems |
| title_full | Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems |
| title_fullStr | Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems |
| title_full_unstemmed | Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems |
| title_short | Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems |
| title_sort | efficient high order iterative methods for solving nonlinear systems and their application on heat conduction problems |
| url | http://dx.doi.org/10.1155/2017/6457532 |
| work_keys_str_mv | AT aliciacordero efficienthighorderiterativemethodsforsolvingnonlinearsystemsandtheirapplicationonheatconductionproblems AT esthergomez efficienthighorderiterativemethodsforsolvingnonlinearsystemsandtheirapplicationonheatconductionproblems AT juanrtorregrosa efficienthighorderiterativemethodsforsolvingnonlinearsystemsandtheirapplicationonheatconductionproblems |