scholarly journals Fractional Pseudo-newton Method and its use in the Solution of a Nonlinear System that Allows the Construction of a Hybrid Solar Receiver

2020 ◽  
Vol 7 (2) ◽  
pp. 01-12
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz ◽  
P. M. Rodrigo ◽  
E. De-la-Vega
Keyword(s):  
Nonlinear System ◽  
Newton Method ◽  
Solar Receiver

The Pressure and Film Thickness Distributions in Point Elastohydrodynamic Contact Under Dynamic Load

2005 ◽  
Author(s):  
M. Ya. Panovko
Keyword(s):  
Steady State ◽  
Nonlinear System ◽  
Free Boundary ◽  
Film Thickness ◽  
Newton Method ◽  
Dynamic Load ◽  
Mathematical Formulation ◽  
Point Contact ◽  
System Of Equations ◽  
System Of Integrodifferential Equations

Isothermal elastohydrodynamic (EHD) problem for dynamically loaded lubricated point contact is formulated and studied numerically. Mathematical formulation is based on the time depending nonlinear system of integrodifferential equations. In order to determine the location of the exit (free) boundary the problem is formulated as a problem of complementarity. The dimensionless system of equations and inequalities is solved using Newton method. Peculiarities of the influence of non-steady state (sinusoidal) loading on pressure and film thickness in the point EHD contact are shown.

scholarly journals A Mixed Line Search Smoothing Quasi-Newton Method for Solving Linear Second-Order Cone Programming Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhuqing Gui ◽  
Chunyan Hu ◽  
Zhibin Zhu
Keyword(s):  
Nonlinear System ◽  
Newton Method ◽  
Jordan Algebra ◽  
Line Search ◽  
Primal Problem ◽  
First Order ◽  
Second Order Cone ◽  
Complementarity Condition ◽  
Quasi Newton ◽  
Mixed Line

Firstly, we give the Karush-Kuhn-Tucker (KKT) optimality condition of primal problem and introduce Jordan algebra simply. On the basis of Jordan algebra, we extend smoothing Fischer-Burmeister (F-B) function to Jordan algebra and make the complementarity condition smoothing. So the first-order optimization condition can be reformed to a nonlinear system. Secondly, we use the mixed line search quasi-Newton method to solve this nonlinear system. Finally, we prove the globally and locally superlinear convergence of the algorithm.

scholarly journals Application of Bessel functions and Jacobian free Newton method to solve time-fractional Burger equation

2019 ◽  
Vol 8 (1) ◽  
pp. 688-694
Author(s):  
Kourosh Parand ◽  
Mehran Nikarya
Keyword(s):  
Nonlinear System ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Newton Method ◽  
Spectral Methods ◽  
Bessel Functions ◽  
Burger Equation ◽  
Algebraic Equations ◽  
Liouville Fractional Derivative ◽  
Novel Method

Abstract In this paper, a novel method based on Bessel functions (BF), generalized Bessel functions (GBF), the collocation method and the Jacobian free Newton-Krylov sub-space (JFNK) will be introduced to solve the nonlinear time-fractional Burger equation. In this paper, an implicit formula is introduced to calculate Riemann–Liouville fractional derivative of GBFs, that can be very useful in spectral methods. In this work, the nonlinear time-fractional Burger equation is converted to a nonlinear system of algebraic equations via collocation algorithm based on BFs and GBFs without any linearization and descretization methods. Finally, by using JFNK, the solution of this nonlinear system will be achieved. To show the reliability and applicability of the proposed method, we solve some examples of time-fractional Burger equation and compare our results with others.

Investigating Dynamics of One Weakly Nonlinear System with Delay Argument

2018 ◽  
Vol 50 (1) ◽  
pp. 20-38 ◽  
Author(s):  
Denis Ya. Khusainov ◽  
Jozef Diblik ◽  
Jaromir Bashtinec ◽  
Andrey V. Shatyrko
Keyword(s):  
Nonlinear System ◽  
Weakly Nonlinear ◽  
Delay Argument ◽  
System With Delay ◽  
Weakly Nonlinear System
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