Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear Systems
Some Kurchatov-type accelerating parameters are used to construct some derivative-free iterative methods with memory for solving nonlinear systems. New iterative methods are developed from an initial scheme without memory with order of convergence three. New methods have the convergence order <in...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-05-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/13/6/943 |
| id |
doaj-7385d856d80b4fcb86af8341aa18975a |
|---|---|
| record_format |
Article |
| spelling |
doaj-7385d856d80b4fcb86af8341aa18975a2021-06-01T01:11:59ZengMDPI AGSymmetry2073-89942021-05-011394394310.3390/sym13060943Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear SystemsXiaofeng Wang0Yingfanghua Jin1Yali Zhao2School of Mathematical Sciences, Bohai University, Jinzhou 121000, ChinaSchool of Mathematical Sciences, Bohai University, Jinzhou 121000, ChinaSchool of Mathematical Sciences, Bohai University, Jinzhou 121000, ChinaSome Kurchatov-type accelerating parameters are used to construct some derivative-free iterative methods with memory for solving nonlinear systems. New iterative methods are developed from an initial scheme without memory with order of convergence three. New methods have the convergence order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>+</mo><msqrt><mn>5</mn></msqrt><mo>≈</mo><mn>4.236</mn></mrow></semantics></math></inline-formula> and 5, respectively. The application of new methods can solve standard nonlinear systems and nonlinear ordinary differential equations (ODEs) in numerical experiments. Numerical results support the theoretical results.https://www.mdpi.com/2073-8994/13/6/943Kurchatov’s methodnonlinear systemsderivative-freeiterative method |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xiaofeng Wang Yingfanghua Jin Yali Zhao |
| spellingShingle |
Xiaofeng Wang Yingfanghua Jin Yali Zhao Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear Systems Symmetry Kurchatov’s method nonlinear systems derivative-free iterative method |
| author_facet |
Xiaofeng Wang Yingfanghua Jin Yali Zhao |
| author_sort |
Xiaofeng Wang |
| title |
Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear Systems |
| title_short |
Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear Systems |
| title_full |
Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear Systems |
| title_fullStr |
Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear Systems |
| title_full_unstemmed |
Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear Systems |
| title_sort |
derivative-free iterative methods with some kurchatov-type accelerating parameters for solving nonlinear systems |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2021-05-01 |
| description |
Some Kurchatov-type accelerating parameters are used to construct some derivative-free iterative methods with memory for solving nonlinear systems. New iterative methods are developed from an initial scheme without memory with order of convergence three. New methods have the convergence order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>+</mo><msqrt><mn>5</mn></msqrt><mo>≈</mo><mn>4.236</mn></mrow></semantics></math></inline-formula> and 5, respectively. The application of new methods can solve standard nonlinear systems and nonlinear ordinary differential equations (ODEs) in numerical experiments. Numerical results support the theoretical results. |
| topic |
Kurchatov’s method nonlinear systems derivative-free iterative method |
| url |
https://www.mdpi.com/2073-8994/13/6/943 |
| work_keys_str_mv |
AT xiaofengwang derivativefreeiterativemethodswithsomekurchatovtypeacceleratingparametersforsolvingnonlinearsystems AT yingfanghuajin derivativefreeiterativemethodswithsomekurchatovtypeacceleratingparametersforsolvingnonlinearsystems AT yalizhao derivativefreeiterativemethodswithsomekurchatovtypeacceleratingparametersforsolvingnonlinearsystems |
| _version_ |
1721412873493676032 |