Optimal parametric families of derivative free iterative structures for locating nonlinear equation solution
محورهای موضوعی : Numerical ComputationOghovese Ogbereyivwe 1 , Salisu Umar 2
1 - Depatment of Mathematics, Faculty of Sciences, Delta State University of Science and Tech., Ozoro, Nigeria
2 - Auchi Polytechnic, Auchi, Nigeria.
کلید واژه: Iterative structure, Nonlinear equation, Steffenson method, optimal order of convergence,
چکیده مقاله :
One golden rule in the development of new iterative structure for locating the solution of nonlinear equation is that, it should beof low computation cost. The presence of functions derivatives evaluations in an iterative structure no doubt, increases its implementationcost. More so, obtaining derivative of some complex functions can be bigchallenge. In this regard, three class of fourth, seventh and eight-orderderivative free iterative structures are developed and put forward inthis manuscript.The convergence test on the developed iterative structures were established using some designed computer programs that areexecuted in MATHEMATICA software environment. Some nonlinearproblems were solved using the developed iterative structures and results obtained were placed in juxtaposition with that of some existingcontemporary methods.
One golden rule in the development of new iterative structure for locating the solution of nonlinear equation is that, it should beof low computation cost. The presence of functions derivatives evaluations in an iterative structure no doubt, increases its implementationcost. More so, obtaining derivative of some complex functions can be bigchallenge. In this regard, three class of fourth, seventh and eight-orderderivative free iterative structures are developed and put forward inthis manuscript.The convergence test on the developed iterative structures were established using some designed computer programs that areexecuted in MATHEMATICA software environment. Some nonlinearproblems were solved using the developed iterative structures and results obtained were placed in juxtaposition with that of some existingcontemporary methods.
