Nonlinear equations with degenerate operator at fractional Caputo derivative
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.3830
Abstract: At first, the existence of a unique solution for the Cauchy problem to nondegenerate fractional differential equation was proved. These results were used for research of the unique solvability for the initial Cauchy and Showalter–Sidorov… read more here.
Keywords: caputo derivative; operator fractional; nonlinear equations; fractional caputo ... See more keywords
Doubly Nonlinear Equations of Porous Medium Type
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DOI: 10.1007/s00205-018-1221-9
Abstract: AbstractIn this paper we prove the existence of solutions to doubly nonlinear equations whose prototype is given by $$\partial_t u^m- {\rm div}\, D_{\xi}\, f(x,Du) =0,$$∂tum-divDξf(x,Du)=0,with $${m\in (0,\infty )}$$m∈(0,∞) , or more generally with an increasing… read more here.
Keywords: medium type; nonlinear equations; doubly nonlinear; equations porous ... See more keywords
Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations
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DOI: 10.1007/s10589-020-00230-x
Abstract: In the case of singular (and possibly even nonisolated) solutions of nonlinear equations, while superlinear convergence of the Newton method cannot be guaranteed, local linear convergence from large domains of starting points still holds under… read more here.
Keywords: convergence; newton method; nonlinear equations; solutions nonlinear ... See more keywords
A general class of four parametric with- and without memory iterative methods for nonlinear equations
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Chemistry"
DOI: 10.1007/s10910-018-00996-w
Abstract: In this paper, we have constructed a derivative-free weighted eighth-order iterative class of methods with and without-memory for solving nonlinear equations. These methods are optimal as they satisfy Kung–Traub’s conjecture. We have used four accelerating… read more here.
Keywords: order; general class; nonlinear equations; without memory ... See more keywords
Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations
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DOI: 10.1007/s11075-021-01112-x
Abstract: For nonlinear equations, the homotopy methods (continuation methods) are popular in engineering fields since their convergence regions are large and they are quite reliable to find a solution. The disadvantage of the classical homotopy methods… read more here.
Keywords: time; continuation newton; nonlinear equations; residual trust ... See more keywords
A hybridization of grey wolf optimizer and differential evolution for solving nonlinear systems
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DOI: 10.1007/s12530-019-09291-8
Abstract: This paper proposes a new algorithm for solving systems of complex nonlinear equations as an optimization problem. A hybridization algorithm from two inspired algorithms, grey wolf optimizer (GWO) and differential evolution (DE) is named GWO-DE.… read more here.
Keywords: optimization; grey wolf; nonlinear equations; differential evolution ... See more keywords
Review of some iterative methods for solving nonlinear equations with multiple zeros
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DOI: 10.1007/s13370-018-00650-3
Abstract: In this paper, some iterative methods with third order convergence for solving the nonlinear equation were reviewed and analyzed. The purpose is to find the best iteration schemes that have been formulated thus far. Hence,… read more here.
Keywords: iterative methods; equations multiple; review iterative; methods solving ... See more keywords
Hessian estimates for fully nonlinear equations via the large-M-inequality principle
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.123953
Abstract: Abstract The approach using the large-M-inequality principle introduced by Acerbi and Mingione [2] has been broadly used in W 1 , p -regularity theory for nonlinear equations in divergence form. We apply this approach to… read more here.
Keywords: fully nonlinear; large inequality; hessian estimates; nonlinear equations ... See more keywords
Boundedness of stable solutions to nonlinear equations involving the p-Laplacian
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DOI: 10.1016/j.jmaa.2020.124122
Abstract: Abstract We consider stable solutions to the equation − Δ p u = f ( u ) in a smooth bounded domain Ω ⊂ R n for a C 1 nonlinearity f. Either in the… read more here.
Keywords: stable solutions; involving laplacian; nonlinear equations; solutions nonlinear ... See more keywords
Two neural dynamics approaches for computing system of time-varying nonlinear equations
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DOI: 10.1016/j.neucom.2020.02.011
Abstract: Abstract The problem of solving time-varying nonlinear equations has received much attention in many fields of science and engineering. In this paper, firstly, considering that the classical gradient-based neural dynamics (GND) might result in nonnegligible… read more here.
Keywords: neural dynamics; time varying; nonlinear equations; model ... See more keywords
Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions.
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DOI: 10.1063/1.5019754
Abstract: A study of rogue-wave solutions in the reverse-time nonlocal nonlinear Schrödinger (NLS) and nonlocal Davey-Stewartson (DS) equations is presented. By using Darboux transformation (DT) method, several types of rogue-wave solutions are constructed. Dynamics of these… read more here.
Keywords: nonlocal nonlinear; wave solutions; reverse time; time ... See more keywords