Abstract
We develop a sixth order Steffensen-type method with one parameter in order to solve systems of equations. Our study’s novelty lies in the fact that two types of local convergence are established under weak conditions, including computable error bounds and uniqueness of the results. The performance of our methods is discussed and compared to other schemes using similar information. Finally, very large systems of equations (100×100 and 200×200) are solved in order to test the theoretical results and compare them favorably to earlier works.
Highlights
IntroductionA plenty of problems from Biology, Chemistry, Economics, Engineering, Mathematics, and Physics are converted to a mathematical expression of the following form
A plenty of problems from Biology, Chemistry, Economics, Engineering, Mathematics, and Physics are converted to a mathematical expression of the following form F (u) = 0. (1)Here, F : Ω ⊂ B → B, is differentiable, B is a Banach space and Ω is nonempty and open
Closed form solutions are rarely found, so iterative methods [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] are used converging to the solution u∗
Summary
A plenty of problems from Biology, Chemistry, Economics, Engineering, Mathematics, and Physics are converted to a mathematical expression of the following form. F : Ω ⊂ B → B, is differentiable, B is a Banach space and Ω is nonempty and open. Closed form solutions are rarely found, so iterative methods [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] are used converging to the solution u∗. U0 ∈ Ω is an initial point and λ ∈ R is a free parameter. We present the advantages over other methods using similar information
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