Applications Of HAM And HPM To Nonlinear Equations

With the development of modern science and technology, there are more and more nonlinear problems in the fields of science and engineering calculation. This paper mainly studies the application of methods to different equations. We deduce new formulas by modifying the formulas or get new method, or deduce perfect iterative formulas. Convergence and rate of convergence of new methods are analyzed. On basis of theoretical studies, we compare with other methods by numerical experiments. Matlab is used mainly. Major achievements are following:(1)In the history to solve nonlinear equations, Newton iterative method and its anamorphosis are classical methods to solve nonlinear equations which are elementary and important until now. It is important to analyze the new iterative formulas which are deduced in According to the quadrature rules by Nenad Ujevic. In consideration of derivative computation and method's rate of convergence, which limit application, we modify the formulas by Steffensen acceleration method and deduce a new class of nonlinear iterative methods without derivatives. The numerical experiments show that new methods without derivative are very effective.(2)Thought essential modification above-mentioned, iterative formula we got low complexity and improve the rate of convergence, but range of application is limited. Bisection method proves nice asymptotic quadratic convergence property and global convergence property of intervals diameters sequence. Combining bisection method, we deduce new formulas and the advantage is showed by numerical experiments.(3)HPM is a new method to solve nonlinear equations. Firstly, we discuss the theoretical knowledge of HPM. Secondly, On the basis of research, study on HPM and its modifications, study the application of HPM to nonlinear equations and deduce the new iterative formulas. The numerical experiments show the advantages of the improved model.