A Class of Collocation Methods for Second Order Ordinary Differential Equation

Extensive use of second-order ordinary differential equations in mathematics, physics, engineering , not bad for the numerical solution of the long Hing , at home and abroad the emergence of a series of important research results . In 2009 , Gonzalez, et al proposed a class on a rigid order equation containing a free parameter , strong A new method , this method is compared with the existing methods , there are a lot of very good character . Firstly, this method is applied to the initial value problem of second order differential equations , indirect configuration methods , and then based on the idea of Gonzalez and others choose the configuration parameters , construct a direct allocation method of second order differential equations , and gives them the order and stability of the results . We found that when the method of series 3 , direct configuration and indirect configuration terraces are 3 ; method of progression is greater than 4:00 , the direct allocation method using the same configuration is one order higher than the indirect configuration terrace . Also , due to the stable region of the four direct configuration method is very limited , so in the fourth chapter we further investigated with two free parameters , more generally , heads explicit , precise rigid four direct configuration . In general , this type of method terrace indirect configuration , the order level no longer increases , we also study the order and stability of such methods by a computer search to find some stability to the region relatively large , has certain advantages for rigid equations . In the fifth chapter, we do two numerical experiments , the case of a non-rigid scalar equations , one case of rigid strong equations , MATLAB programming through the use of technology , we found that the good results of the calculation results with the theoretical analysis maintained the same.