کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4642076 | 1341330 | 2008 | 17 صفحه PDF | دانلود رایگان |
Algebraic and differential equations generally co-build mathematical models. Either lack or intractability of their analytical solution often forces workers to resort to an iterative method and face the likely challenges of slow convergence, non-convergence or even divergence. This manuscript presents a novel class of third-order iterative techniques in the form of xk+1=gu(xk)=xk+f(xk)u(xk)xk+1=gu(xk)=xk+f(xk)u(xk) to solve a nonlinear equation f with the aid of a weight function u. The class currently contains an invert-and-average (gKia)(gKia), an average-and-invert (gKai)(gKai), and an invert-and-exponentiate (gKe)(gKe) branch. Each branch has several members some of which embed second-order Newton's (gN)(gN), third-order Chebychev's (gC)(gC) or Halley's (gH)(gH) solvers. Class members surpassed stand-alone applications of these three well-known methods. Other methods are also permitted as auxiliaries provided they are at least of second order. Asymptotic convergence constants are calculated. Assignment of class parameters to non-members carries them to a common basis for comparison. This research also generated a one-step “solver” that is usable for post-priori analysis, trouble shooting, and comparison.
Journal: Journal of Computational and Applied Mathematics - Volume 218, Issue 2, 1 September 2008, Pages 290–306