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...
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| Format: | Article |
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MDPI AG
2021-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/6/943 |
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| author | Xiaofeng Wang Yingfanghua Jin Yali Zhao |
| author_facet | Xiaofeng Wang Yingfanghua Jin Yali Zhao |
| author_sort | Xiaofeng Wang |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T11:01:30Z |
| format | Article |
| id | doaj.art-7385d856d80b4fcb86af8341aa18975a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T11:01:30Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7385d856d80b4fcb86af8341aa18975a2023-11-21T21:28:40ZengMDPI AGSymmetry2073-89942021-05-0113694310.3390/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 |
| 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 |
| title | 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_short | 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 |
| topic | Kurchatov’s method nonlinear systems derivative-free iterative method |
| url | https://www.mdpi.com/2073-8994/13/6/943 |
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