Browsing by Author "Sheth, S.M."
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Item The asymptotic mesh independence principle of Newton's method under weaker conditions(2016) Argyros, I.K.; Sheth, S.M.; Younis, R.M.; George, S.We present a new asymptotic mesh independence principle of Newton's method for discretized nonlinear operator equations. Our hypotheses are weaker than in earlier studies such as [1], [8]-[12]. This way we extend the applicability of the mesh independence principle which asserts that the behavior of the discretized version is asymptotically the same as that of the original iteration and consequently, the number of steps required by the two processes to converge within a given tolerance is essentially the same. The results apply to solve a boundary value problem that cannot be solved with the earlier hypotheses given in [12]. 2016 International Publications. All rights reserved.Item Extending the Mesh Independence For Solving Nonlinear Equations Using Restricted Domains(2017) Argyros, I.K.; Sheth, S.M.; Younis, R.M.; Magre n, .A.; George, S.The mesh independence principle states that, if Newton s method is used to solve an equation on Banach spaces as well as finite dimensional discretizations of that equation, then the behaviour of the discretized process is essentially the same as that of the initial method. This principle was inagurated in Allgower et al. (SIAM J Numer Anal 23(1):160 169, 1986). Using our new Newton Kantorovich-like theorem and under the same information we show how to extend the applicability of this principle in cases not possible before. The results can be used to provide more efficient programming methods. 2017, Springer (India) Private Ltd.Item Extending the Mesh Independence For Solving Nonlinear Equations Using Restricted Domains(Springer, 2017) Argyros, I.K.; Sheth, S.M.; Younis, R.M.; Magreñán Ruiz, Á.A.; George, S.The mesh independence principle states that, if Newton’s method is used to solve an equation on Banach spaces as well as finite dimensional discretizations of that equation, then the behaviour of the discretized process is essentially the same as that of the initial method. This principle was inagurated in Allgower et al. (SIAM J Numer Anal 23(1):160–169, 1986). Using our new Newton–Kantorovich-like theorem and under the same information we show how to extend the applicability of this principle in cases not possible before. The results can be used to provide more efficient programming methods. © 2017, Springer (India) Private Ltd.Item The asymptotic mesh independence principle of Newton's method under weaker conditions(International Publications internationalpubls@yahoo.com, 2016) Argyros, I.K.; Sheth, S.M.; Younis, R.M.; George, S.We present a new asymptotic mesh independence principle of Newton's method for discretized nonlinear operator equations. Our hypotheses are weaker than in earlier studies such as [1], [8]-[12]. This way we extend the applicability of the mesh independence principle which asserts that the behavior of the discretized version is asymptotically the same as that of the original iteration and consequently, the number of steps required by the two processes to converge within a given tolerance is essentially the same. The results apply to solve a boundary value problem that cannot be solved with the earlier hypotheses given in [12]. © 2016 International Publications. All rights reserved.