An efficient family of Steffensen‐type methods with memory for solving systems of nonlinear equations. Issue 6 (10th October 2021)

• Record Type: Journal Article
• Authors: Narang, Mona; Bhatia, Saurabh; Kanwar, Vinay
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 6(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-10-10
• Subjects: computational efficiency -- derivative‐free methods -- order of convergence -- Steffensen's method -- systems of nonlinear equations; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1192
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract: The article discusses derivative‐free algorithms with and without memory for solving numerically nonlinear systems. We proposed a family of fifth‐ and sixth‐order schemes and extended them to algorithms with memory. We further discuss the convergence and computational efficiency of these algorithms. Numerical examples of mixed Hammerstein integral equation, discrete nonlinear ordinary differential equation, and Fisher's partial differential equation with Neumann's boundary conditions are discussed to demonstrate the convergence and efficiency of these schemes. Finally, some numerical results are included to examine the performance of the developed methods.