Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering

In this paper, we propose two novel iteration schemes for computing zeros of nonlinear equations in one dimension. We develop these iteration schemes with the help of Taylor’s series expansion, generalized Newton-Raphson’s method, and interpolation technique. The convergence analysis of the proposed iteration schemes is discussed. It is established that the newly developed iteration schemes have sixth order of convergence. Several numerical examples have been solved to illustrate the applicability and validity of the suggested schemes. These problems also include some real-life applications associated with the chemical and civil engineering such as adiabatic flame temperature equation, conversion of nitrogen-hydrogen feed to ammonia, the van der Wall’s equation, and the open channel flow problem whose numerical results prove the better efficiency of these methods as compared to other well-known existing iterative methods of the same kind.