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New Trends in Differential and Difference Equations and Applications

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ISBN: 9783039215386 / 9783039215393 Year: Pages: 198 DOI: 10.3390/books978-3-03921-539-3 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:15
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Abstract

This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

Keywords

Legendre wavelets --- collocation method --- three-step Taylor method --- asymptotic stability --- time-dependent partial differential equations --- non-instantaneous impulses --- Caputo fractional derivative --- differential equations --- state dependent delays --- lipschitz stability --- limit-periodic solutions --- difference equations --- exponential dichotomy --- strong nonlinearities --- effective existence criteria --- population dynamics --- discrete Lyapunov equation --- difference equations --- Hilbert space --- dichotomy --- exponential stability --- ?-Laplacian operator --- mean curvature operator --- heteroclinic solutions --- problems in the real line --- lower and upper solutions --- Nagumo condition on the real line --- fixed point theory --- coupled nonlinear systems --- functional boundary conditions --- Schauder’s fixed point theory --- Arzèla Ascoli theorem --- lower and upper solutions --- first order periodic systems --- SIRS epidemic model --- mathematical modelling --- Navier–Stokes equations --- global solutions --- regular solutions --- a priori estimates --- weak solutions --- kinetic energy --- dissipation --- Bäcklund transformation --- Clairin’s method --- generalized Liouville equation --- Miura transformation --- Korteweg-de Vries equation --- second-order differential/difference/q-difference equation of hypergeometric type --- non-uniform lattices --- divided-difference equations --- polynomial solution --- integro-differentials --- Sumudu decomposition method --- dynamical system

Inequalities

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ISBN: 9783039280629 / 9783039280636 Year: Pages: 204 DOI: 10.3390/books978-3-03928-063-6 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics --- Science (General)
Added to DOAB on : 2020-01-30 16:39:46
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Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.

Keywords

analytic functions --- starlike functions --- convex functions --- Fekete-Szegö inequality --- Hilbert C*-module --- g-frame --- g-Bessel sequence --- adjointable operator --- analytic functions --- starlike functions --- convex functions --- Fekete-Szegö inequality --- operator inequality --- positive linear map --- operator Kantorovich inequality --- geometrically convex function --- frame --- weaving frame --- weaving frame operator --- alternate dual frame --- Hilbert space --- quantum estimates --- Hermite-Hadamard type inequalities --- quasi-convex --- Hermite–Hadamard type inequality --- strongly ?-convex functions --- Hölder’s inequality --- Power mean inequality --- Katugampola fractional integrals --- Riemann–Liouville fractional integrals --- Hadamard fractional integrals --- Steffensen’s inequality --- higher order convexity --- Green functions --- Montgomery identity --- Fink’s identity --- Hermite-Hadamard inequality --- interval-valued functions --- (h1, h2)-convex --- majorization inequality --- twice differentiable convex functions --- refined inequality --- Taylor theorem --- Gronwall–Bellman inequality --- proportional fractional derivative --- Riemann–Liouville and Caputo proportional fractional initial value problem --- convex functions --- Fejér’s inequality --- special means --- weaving frame --- weaving K-frame --- K-dual --- pseudo-inverse --- ?-variation --- one-sided singular integral --- commutator --- one-sided weighted Morrey space --- one-sided weighted Campanato space --- power inequalities --- exponential inequalities --- trigonometric inequalities --- weight function --- half-discrete Hardy-Hilbert’s inequality --- parameter --- Euler-Maclaurin summation formula --- reverse inequality

Evolutionary Computation

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ISBN: 9783039219285 / 9783039219292 Year: Pages: 424 DOI: 10.3390/books978-3-03921-929-2 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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Computational intelligence is a general term for a class of algorithms designed by nature's wisdom and human intelligence. Computer scientists have proposed many computational intelligence algorithms with heuristic features. These algorithms either mimic the evolutionary processes of the biological world, mimic the physiological structure and bodily functions of the organism,

Keywords

artificial bee colony algorithm (ABC) --- cloud model --- normal cloud model --- Y conditional cloud generator --- global optimum --- evolution --- computation --- urban design --- biology --- shape grammar --- architecture --- SPEA 2 --- energy-efficient job shop scheduling --- dispatching rule --- nonlinear convergence factor --- mutation operation --- whale optimization algorithm --- particle swarm optimization --- confidence term --- random weight --- benchmark functions --- t-test --- success rates --- average iteration times --- set-union knapsack problem --- moth search algorithm --- transfer function --- discrete algorithm --- evolutionary multi-objective optimization --- convergence point --- acceleration search --- evolutionary computation --- optimization --- bat algorithm (BA) --- bat algorithm with multiple strategy coupling (mixBA) --- CEC2013 benchmarks --- Wilcoxon test --- Friedman test --- facility layout design --- single loop --- monarch butterfly optimization --- slicing tree structure --- material handling path --- integrated design --- wireless sensor networks (WSNs) --- DV-Hop algorithm --- multi-objective DV-Hop localization algorithm --- NSGA-II-DV-Hop --- first-arrival picking --- fuzzy c-means --- particle swarm optimization --- range detection --- minimum total dominating set --- evolutionary algorithm --- genetic algorithm --- local search --- constrained optimization problems (COPs) --- evolutionary algorithms (EAs) --- firefly algorithm (FA) --- stochastic ranking (SR) --- Artificial bee colony --- swarm intelligence --- elite strategy --- dimension learning --- global optimization --- DE algorithm --- ?-Hilbert space --- topology structure --- quantum uncertainty property --- numerical simulation --- whale optimization algorithm --- flexible job shop scheduling problem --- nonlinear convergence factor --- adaptive weight --- variable neighborhood search --- elephant herding optimization --- EHO --- swarm intelligence --- individual updating strategy --- large-scale --- benchmark --- diversity maintenance --- particle swarm optimizer --- entropy --- large scale optimization --- minimum load coloring --- memetic algorithm --- evolutionary --- local search --- particle swarm optimization --- large-scale optimization --- adaptive multi-swarm --- diversity maintenance --- deep learning --- convolutional neural network --- rock types --- automatic identification --- monarch butterfly optimization --- greedy optimization algorithm --- global position updating operator --- 0-1 knapsack problems

Iterative Methods for Solving Nonlinear Equations and Systems

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ISBN: 9783039219407 / 9783039219414 Year: Pages: 494 DOI: 10.3390/books978-3-03921-941-4 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-01-07 09:08:26
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Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Keywords

point projection --- intersection --- parametric curve --- n-dimensional Euclidean space --- Newton’s second order method --- fixed point theorem --- nonlinear equations --- multiple zeros --- optimal iterative methods --- higher order of convergence --- nonlinear operator equation --- Fréchet derivative --- ?-continuity condition --- Newton-like method --- Frédholm integral equation --- nonlinear equations --- Padé approximation --- iterative method --- order of convergence --- numerical experiment --- fourth order iterative methods --- local convergence --- banach space --- radius of convergence --- nonlinear equation --- iterative process --- non-differentiable operator --- Lipschitz condition --- high order --- sixteenth order convergence method --- local convergence --- dynamics --- Banach space --- Newton’s method --- semi-local convergence --- Kantorovich hypothesis --- iterative methods --- Steffensen’s method --- R-order --- with memory --- computational efficiency --- non-linear equation --- basins of attraction --- optimal order --- higher order method --- computational order of convergence --- nonlinear equations --- multiple roots --- Chebyshev–Halley-type --- optimal iterative methods --- efficiency index --- Banach space --- semilocal convergence --- ?-continuity condition --- Jarratt method --- error bound --- Fredholm integral equation --- Newton’s method --- global convergence --- variational inequality problem --- split variational inclusion problem --- multi-valued quasi-nonexpasive mappings --- Hilbert space --- sixteenth-order optimal convergence --- multiple-root finder --- asymptotic error constant --- weight function --- purely imaginary extraneous fixed point --- attractor basin --- drazin inverse --- generalized inverse --- iterative methods --- higher order --- efficiency index --- integral equation --- efficiency index --- nonlinear models --- iterative methods --- higher order --- nonlinear equations --- optimal iterative methods --- multiple roots --- efficiency index --- iterative methods --- nonlinear equations --- Newton-type methods --- smooth and nonsmooth operators --- heston model --- Hull–White --- option pricing --- PDE --- finite difference (FD) --- iteration scheme --- Moore–Penrose --- rectangular matrices --- rate of convergence --- efficiency index --- nonlinear equations --- conjugate gradient method --- projection method --- convex constraints --- signal and image processing --- nonlinear monotone equations --- conjugate gradient method --- projection method --- signal processing --- nonlinear systems --- multipoint iterative methods --- divided difference operator --- order of convergence --- Newton’s method --- computational efficiency index --- system of nonlinear equations --- Newton method --- Newton-HSS method --- nonlinear HSS-like method --- Picard-HSS method --- convexity --- least square problem --- accretive operators --- signal processing --- point projection --- intersection --- planar algebraic curve --- Newton’s iterative method --- the improved curvature circle algorithm --- systems of nonlinear equations --- King’s family --- order of convergence --- multipoint iterative methods --- nonlinear equations --- Potra–Pták method --- optimal methods --- weight function --- basin of attraction --- engineering applications --- Kung–Traub conjecture --- multipoint iterations --- nonlinear equation --- optimal order --- basins of attraction

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