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Wednesday, August 5, 2020 | History

2 edition of iterative procedure for the solution of nonlinear equations in a Banach space found in the catalog.

iterative procedure for the solution of nonlinear equations in a Banach space

Sergei Kalvin Aalto

# iterative procedure for the solution of nonlinear equations in a Banach space

## by Sergei Kalvin Aalto

Published .
Written in English

Subjects:
• Banach spaces.

• Edition Notes

The Physical Object ID Numbers Statement by Sergei Kalvin Aalto. Pagination , 62 leaves, bound : Number of Pages 62 Open Library OL14259212M

Some fourth-order iterative methods for solving non-linear equations, Appl. Math. Lett., , (), Solution of Equation in Euclidean and Banach Space, 3 rd edition, Academic Press, New York, Three new iterative methods for solving nonlinear equations, Australian Journal of Basic and Applied Sciences, 4(6), (). We examined a general method for obtaining a solution to a class of monotone variational inequalities in Hilbert space. Let H be a real Hilbert space, and Let T: H -> H be a continuous linear monotone operator and K be a non empty closed convex subset of H. From an initial arbitrary point x 0 ∈ K. We proposed and obtained iterative method that converges in norm to a solution of the class of.

The solutions generated by NDSolve, Mathematica's function for numerical solution of ordinary and partial differential equations, are (interpolating) functions. This unique feature of Mathematica enables the implementation of iterative solution methods for nonlinear boundary value differential equations in a straightforward fashion. We also investigate the Ulam-Hyers and Ulam-Hyers-Rassias stability of similar solutions. These results are established in Banach space with the help of resolvent operator functions and fixed point technique on an unbounded interval. An example is also presented for the illustration of obtained results.

The coupled nonlinear matrix integral equations for the matrices X (z) and Y (z) which factor the dispersion matrix Λ (z) of multigroup transport theory are studied in a Banach space utilizing fixed‐point theorems we are able to show that iterative solutions converge uniquely to the ’’physical solution’’ in a certain sphere of isotropic and anisotropic scattering are. Substitute the value of the variable into the nonlinear equation. When you plug 3 + 4y into the second equation for x, you get (3 + 4y)y = Solve the nonlinear equation for the variable. When you distribute the y, you get 4y 2 + 3y = 6. Because this equation is quadratic, you must get 0 on one side, so subtract the 6 from both sides to get 4y 2 + 3y – 6 = You have to use the.

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### Iterative procedure for the solution of nonlinear equations in a Banach space by Sergei Kalvin Aalto Download PDF EPUB FB2

Solution of dense linear systems as described in standard texts such as , [],or[]. Our approach is to focus on a small number of methods and treat them in depth. Though this book is written in a ﬁnite-dimensional setting, we have selected for coverage mostlyalgorithms and methods of analysis whichFile Size: KB.

This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides.

We investigate the initial value problem for a class of fractional evolution equations in a Banach space. Under some monotone conditions and noncompactness measure conditions of the nonlinearity, the well-known monotone iterative technique is then extended for fractional evolution equations which provides computable monotone sequences that converge to the extremal solutions in a sector Cited by:   These results are inspired They can be used to derive by [4, Theorems and ].

sets. iterative procedures for the construction of zeros of accretive The first ergodic theorems for nonlinear nonexpansive map^ pings and semigroups in Hilbert space were established by Bâillon S.

RElCH and by B a i l l o n and B r g z i s [ l ].Cited by:   G.A. Anastassiou, I.K. Argyros, Generalized Iterative procedures and their applications to Banach space valued functions in abstract fractional calculus (submitted, ) Google Scholar 6.

I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach : George A. Anastassiou, Ioannis K.

Argyros. Through solving equations step by step and by using the generalized Banach fixed point theorem, under simple conditions, the authors present the existence and uniqueness theorem of the iterative.

This book is devoted to the approximation of nonlinear equations using iterative methods. This area, as a subﬁeld of Applied Mathematics, remains an active branch of research.

Many problems in Computational Sciences and other disciplines can be stated in the form of a nonlinear equation or system using mathematical modeling. In this research, some iterative methods used to approximate common fixed points of some nonlinear operators in Banach space are introduced and studied.

In particular, modified iterative schemes for fixed point of family of asymptotically nonexpansive mappings are introduced and studied. Therefrom, strong. If the nonlinear system has no solution, the method attempts to find a solution in the non-linear least squares sense. See Gauss–Newton algorithm for more information.

Nonlinear equations in a Banach space. Another generalization is Newton's method to find a root of a functional F defined in a Banach space. In this case the formulation is. In this paper, we study the existence and uniqueness of extremal mild solutions for finite delay differential equations of fractional order in Banach spaces with the help of the monotone iterative.

References. Abbasbandy, “Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method,” Applied Mathematics and Computation, vol. no.pp. –, View at: Publisher Site | Google Scholar | Zentralblatt MATH G.

Adomian, Nonlinear Stochastic Systems and Applications to Physics, vol. 46 of Mathematics and Its Applications, Kluwer. of a nonlinear equation in a Banach space setting. Our methods include the Halley and other high order point, to give conditions ensuring the convergence of the iterative procedure; while the local one is, based In particular, the practice of Numerical Functional Analysis for nding solution x of equation () is essentially connected to.

SIAM Journal on Numerical Analysis. Article Tools. Add to my favorites. The method of discretization is used to solve nonlinear equations involving Banach space valued operators using Lipschitz or Hölder constants. But these constants cannot always be found.

That is why we present results using ω− continuity conditions on the Fréchet derivative of the operator involved. This way, we extend the applicability of the discretization technique.

() Iterative algorithms for solutions of Hammerstein equations in real Banach spaces. Fixed Point Theory and Applications () Strong convergence of an inertial iterative algorithm for variational inequality problem, generalized equilibrium problem, and fixed point problem in a Banach space.

Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution.

Originally published init offers a research-level presentation of the principal results known at that time. The Banach fixed point theorem is a useful technique to investigate the existence and uniqueness of the solution of fuzzy Volterra integral equations (see [6, 7, 21, 36, 38]), while the Darbo fixed-points theorem is an appropriate technique to prove the existence of solutions for fuzzy Volterra integral equation (see).

Some problems of fuzzy. Iterative method for solving nonlinear equations: finding approximate solutions The more we substitute values into the formula, the closer we get to the actual solution to the equation.

We want to get to a stage where the value of xn is equal to the value xn+1 to a given degree of accuracy. Hao, L. Liu and Y. Wu, Iterative solution for nonlinear impulsive advection reaction diffusion equations, J.

Nonlinear Sci. Appl. 9 (6) (), –  X. Hao and L. Liu, Mild solutions of impulsive semilinear neutral evolution equations in Banach spaces, J. Nonlinear Sci. Appl. 9 (12) (), – . An iterative procedure for the solution of nonlinear equations in a Banach space Public Deposited.

Analytics × Add to InZarantonello published a constructive method for the solution of certain nonlinear problems in a Hilbert space.

We extend the method in various directions including a generalization to a Banach space setting. point equation in an appropriate function space. Namely, by applying Green’s function g for the differential operator-Asubject to Dirichlet boundary con-ditions, problem (1) is transformed into the nonlinear integral equation of Hammersteintype (2) u(x) fn g(x,y)f(y,u(y))dy, x.

This integral equation can be considered as a fixed point. We obtain necessary and sufficient conditions for the existence of solutions of weakly nonlinear boundary-value problems for differential equations in a Banach space.

A convergent iterative procedure is proposed for the determination of solutions. We also establish a relationship between necessary and sufficient conditions.Iterative Methods for Approximate Solution of Inverse Problems Alexander Balanov, Natalia Janson, Dmitry Postnov, Olga Sosnovtseva This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods.