Simple and efficient fifth order solvers for systems of nonlinear problems

• Published in: Mathematical modelling and analysis Vol. 28; no. 1; pp. 1 - 22
• Main Authors: Singh, Harmandeep, Sharma, Janak Raj
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 01.01.2023
• Subjects: Algorithms; Approximation; computational complexity; Computational efficiency; Computing costs; Convergence (Mathematics); convergence order; Differential equations, Nonlinear; Efficiency; Iterative methods; iterative techniques; Mathematical research; Neighborhoods; Nonlinear equations; Nonlinear systems; India; nonlinear systems; convergence order; iterative techniques; computational complexity
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2023.16244

In this study, two multi-step iterative techniques of fifth order convergence are explored to solve nonlinear equations. The techniques are designed with the prime objective of keeping the computational cost as low as possible. To claim this objective, the efficiency indices are determined and compared with the efficiencies of the existing techniques of same order. The outcome of comparison analysis is remarkable from the view of high computational efficiency of new methods. Performance and stability are illustrated by executing the numerical tests on some nonlinear problems of diverse nature. The entire analysis significantly favors the new techniques compared to their existing counterparts, especially for the case of large dimensional systems.