A novel adaptive quasi-Newton-type update and its global convergence without Lipschitz condition for constrained system of nonlinear monotone equations. [PDF]
PLoS OneAhmed K +7 more
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Iterated Numerical Homogenization for MultiScale Elliptic Equations with Monotone Nonlinearity [PDF]
Multiscale Modeling & Simulation, 2021 Nonlinear multiscale problems are ubiquitous in materials science and biology. Complicated interactions between nonlinearities and (nonseparable) multiple scales pose a major challenge for analysis and simulation. In this paper, we study the numerical homogenization for multiscale elliptic PDEs with monotone nonlinearity, in particular the Leray--Lions
Xinliang Liu +2 more
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Results in Applied Mathematics, 2019 In this article, we propose a three-term conjugate gradient projection algorithm for solving constrained monotone nonlinear equations. The global convergence of the algorithm was established under suitable assumptions.
Auwal Bala Abubakar +2 more
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Random nonlinear equations and monotonic nonlinearities
Journal of Mathematical Analysis and Applications, 1977 AbstractThe question of existence of random solutions of nonlinear random operator equations involving a monotonic nonlinearity is discussed.
Kannan, R, Salehi, H
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Approximation Schemes for Monotone Systems of Nonlinear Second Order Partial Differential Equations: Convergence Result and Error Estimate [PDF]
, 2012 To appear in Differential Equations and ApplicationsInternational audienceWe consider approximation schemes for monotone systems of fully nonlinear second order partial di erential equations.
Briani, Ariela +5 more
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Positive Decreasing Solutions of Higher-Order Nonlinear Difference Equations
Advances in Difference Equations, 2010 It is shown that the decay rates of the positive, monotone decreasing solutions approaching the zero equilibrium of higher-order nonlinear difference equations are related to the positive characteristic values of the corresponding linearized equation. If
B. Krasznai, I. Győri, M. Pituk
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Nonlinear Differential Equations and Dynamical Systems [PDF]
, 2021 This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse ...
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The approximate solution of a monotone nonlinear operator equations
Rocky Mountain Journal of Mathematics, 1986 This paper is concerned with nonlinear equations involving monotone operators and compact perturbations of monotone operators. Projection methods determine approximate solutions. Such equations are put into the more general framework of regular operator approximation theory, which yields the convergence of approximate solutions under minimal hypothesis.
Anselone, P.M., Jin-gan, Lei
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A method with inertial extrapolation step for convex constrained monotone equations
Journal of Inequalities and Applications, 2021 In recent times, various algorithms have been incorporated with the inertial extrapolation step to speed up the convergence of the sequence generated by these algorithms.
Abdulkarim Hassan Ibrahim +3 more
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A New Conjugate Gradient Projection Method for Convex Constrained Nonlinear Equations
Complexity, 2020 The conjugate gradient projection method is one of the most effective methods for solving large-scale monotone nonlinear equations with convex constraints.
Pengjie Liu, Jinbao Jian, Xianzhen Jiang
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