Fixed-Point Iterative Method with Eighth-Order Constructed by Undetermined Parameter Technique for Solving Nonlinear Systems

Symmetry

Xiaofeng Wang¹ 

[1] School of Mathematical Sciences, Bohai University, Jinzhou 121000, China;

关键词: ordinary differential equations;    partial differential equations;    nonlinear systems;    convergence order;    computational efficiency;    computational cost;   

DOI  :  10.3390/sym13050863

来源: DOAJ

【 摘 要 】

In this manuscript, by using undetermined parameter method, an efficient iterative method with eighth-order is designed to solve nonlinear systems. The new method requires one matrix inversion per iteration, which means that computational cost of our method is low. The theoretical efficiency of the proposed method is analyzed, which is superior to other methods. Numerical results show that the proposed method can reduce the computational time, remarkably. New method is applied to solve the numerical solution of nonlinear ordinary differential equations (ODEs) and partial differential equations (PDEs). The nonlinear ODEs and PDEs are discretized by finite difference method. The validity of the new method is verified by comparison with analytic solutions.

【 授权许可】

Unknown