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A generalized extragradient method for variational inequalities of the second kind
We formulate and analyze a generalized extragradient method for the iterative solution of variational inequalities of the second kind of the form
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Wave Propagation and Soliton Behaviors for the Strain Equation by Using the Sub-ODE Method and Expansion Technique
Within this study, we use the exact techniques to compute the new distinct soliton solutions of the strain wave equation. The governing equation is...
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Hyperbolic Lattice Boltzmann Method and Discrete Boltzmann Method for Solid–Liquid Phase Change Problem
The lattice Boltzmann method (LBM) is a potential numerical tool for solving challenging fluid problems. The Bhatnagar Gross Krook (BGK)...
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Bifurcation Analysis and Soliton Solutions to the Kuralay Equation Via Dynamic System Analysis Method and Complete Discrimination System Method
In this paper, the dynamical system bifurcation theory approach are employed to investigate the phase diagrams of the magnet-optic wave guides in...
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Upper and Lower Solutions Method for Single Equations
In this chapter we introduce the upper and lower solutions method for the boundary value problem of elliptic single equations.
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Partial Newton-Correction Method for Multiple Fixed Points of Semi-linear Differential Operators by Legendre–Gauss–Lobatto Pseudospectral Method
Inspired by several numerical methods for finding multiple solutions, a partial Newton-correction method (PNCM) is proposed to find multiple fixed...
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Traveling Wave Method
AbstractA survey of the development of the traveling wave method for one-dimensional media is presented. The main results and changes in the...
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The exact projective penalty method for constrained optimization
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones....
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Polyak Minorant Method for Convex Optimization
In 1963 Boris Polyak suggested a particular step size for gradient descent methods, now known as the Polyak step size, that he later adapted to...
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An Accelerated Stochastic Mirror Descent Method
Driven by large-scale optimization problems arising from machine learning, the development of stochastic optimization methods has witnessed a huge...
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A Local Macroscopic Conservative (LoMaC) Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics
In this paper, we propose a novel Local Macroscopic Conservative (LoMaC) low rank tensor method with discontinuous Galerkin (DG) discretization for...
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Lehmann–Goerisch Method for High-Precision Eigenvalue Bounds
This chapter provides a deep exploration of the Lehmann–Goerisch method, designed for the efficient computation of high-precision eigenvalue bounds....
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A bundle-type method for nonsmooth DC programs
A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact...
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Meshfree Multiscale Method for Richards’ Equation in Fractured Media
AbstractIn this paper, we develop a meshfree multiscale method for solving the unsaturated filtration problem in fractured media described by...
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A Regular Difference Grid and Characteristics Method
AbstractAn explicit characteristics method used to calculate the values of gas-dynamic parameters (GDP) of one-dimensional unsteady flows is...
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Interior estimates for the virtual element method
We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite...
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Inexact Newton Method for Solving Generalized Nash Equilibrium Problems
In this article, we present an inexact Newton method to solve generalized Nash equilibrium problems (GNEPs). Two types of GNEPs are studied: player...
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An Online Stabilization Method for Parametrized Viscous Flows
The purpose of this work is to investigate the inf-sup stability of reduced basis (RB) method applied to parametric Stokes problem. While performing...
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Upper and Lower Solutions Method for Systems
In this chapter we introduce the Upper and lower solutions method for systems upper and lower solutions method for the boundary value problem of...
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Mathematical Modelling of the Lomb–Scargle Method in Astrophysics
In astrophysics, the Lomb–Scargle method is widely used to analyse time series observations of stellar objects. The method allows us to detect...