Author:
Ahmad Junaid,Arshad Muhammad,Ullah Kifayat,Ma Zhenhua
Abstract
AbstractWe compute the numerical solution of the Bratu’s boundary value problem (BVP) on a Banach space setting. To do this, we embed a Green’s function into a new two-step iteration scheme. After this, under some assumptions, we show that this new iterative scheme converges to a sought solution of the one-dimensional non-linear Bratu’s BVP. Furthermore, we show that the suggested new iterative scheme is essentially weak $w^{2}$
w
2
-stable in this setting. We perform some numerical computations and compare our findings with some other iterative schemes of the literature. Numerical results show that our new approach is numerically highly accurate and stable with respect to different set of parameters.
Funder
Three Three Three Talents Project
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis