Extension of the finite-difference Newton- Raphson algorithm to the simultaneous optimization of trajectories and associated parameters

1968 ◽  
Author(s):  
C. VAN DINE
Keyword(s):  
Finite Difference ◽  
Simultaneous Optimization ◽  
Newton Raphson ◽  
Raphson Algorithm

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

A Class of Decision Processes Showing Policy-Improvement/Newton–Raphson Equivalence

1989 ◽  
Vol 3 (3) ◽  
pp. 397-403 ◽  
Author(s):  
P. Whittle
Keyword(s):  
Optimality Condition ◽  
Regularity Condition ◽  
Decision Processes ◽  
Policy Improvement ◽  
Improvement Algorithm ◽  
Newton Raphson ◽  
Raphson Algorithm

A condition expressed in Eq. (7) is given which, with one simplifying regularity condition, ensures that the policy-improvement algorithm is equivalent to application of the Newton–Raphson algorithm to an optimality condition. It is shown that this condition covers the two known cases of such equivalence, and another example is noted. The condition is believed to be necessary to within transformations of the problem, but this has not been proved.

scholarly journals An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

2013 ◽  
Vol 23 (1) ◽  
pp. 117-129 ◽  
Author(s):  
Jiawen Bian ◽  
Huiming Peng ◽  
Jing Xing ◽  
Zhihui Liu ◽  
Hongwei Li
Keyword(s):  
Parameter Estimation ◽  
Convergence Rate ◽  
Efficient Algorithm ◽  
Numerical Experiments ◽  
Additive Noise ◽  
Mean Squared Errors ◽  
Least Squares Estimators ◽  
The Mean ◽  
Newton Raphson ◽  
Raphson Algorithm

This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton-Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified Newton- Raphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.

Generalized Newton–Raphson algorithm for high dimensional LASSO regression

2021 ◽  
Vol 14 (3) ◽  
pp. 339-350
Author(s):  
Yueyong Shi ◽  
Jian Huang ◽  
Yuling Jiao ◽  
Yicheng Kang ◽  
Hu Zhang
Keyword(s):  
High Dimensional ◽  
Lasso Regression ◽  
Newton Raphson ◽  
Generalized Newton ◽  
Raphson Algorithm

Simulation of a Gas-Dominated, Two-Phase Geothermal Reservoir

1980 ◽  
Vol 20 (01) ◽  
pp. 52-58 ◽  
Author(s):  
G.A. Zyvoloski ◽  
M.J. O'Sullivan
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Gas Content ◽  
Natural State ◽  
Petroleum Reservoir ◽  
Partial Differential ◽  
Geothermal Reservoirs ◽  
Noncondensable Gas ◽  
Newton Raphson

Abstract The basic equations governing the behavior of a two-phase mixture of carbon dioxide (CO2) and water are discussed. A Newton-Raphson scheme, based on the alternating direction implicit (ADI) method for multidimensional problems, is used to solve the nonlinear finite difference approximation of the governing nonlinear system of partial differential equations. Sample calculations showing the behavior of hypothetical reservoirs with varying CO2 contents are presented. Introduction Geothermal reservoirs often contain an appreciable amount of noncondensable gases that have major effects on the behavior of the reservoir in both its natural state and under exploitation. In its natural state, the partial pressure of the noncondensable gas causes the reservoir to boil at a lower temperature than does a pure water field. Under exploitation the presence of CO2 or hydrogen sulfide (the most presence of CO2 or hydrogen sulfide (the most common gases in geothermal fields) dominates the transport and thermodynamical characteristics of the flow. It already has been shown that for lumped parameter models of geothermal reservoirs, small parameter models of geothermal reservoirs, small differences in the CO2 content of the reservoir cause major changes in the pressure, enthalpy, and gas content of the discharge fluid. Because of the importance of the gas content in influencing the design of flash turbines and other geothermal energy conversion systems, it is essential to include the effects of noncondensable gases in simulations of gassy geothermal reservoirs.Most of the procedures developed for simulating the behavior of geothermal reservoirs have features that are not modified easily to include the effects of a noncondensable gas. These difficulties arise either from the numerical procedures used or from the methods of treatment of the thermodynamics of the system. The work of Pritchett et al. uses the fluid (mixture) density and internal energy as primary dependent variables and interpolation between tabular values for determining thermodynamic properties. With the addition of a noncondensable properties. With the addition of a noncondensable gas, the use of density and internal energy (together with one other unknown) leads to an indirect iterative calculation of the other fluid properties such as temperature and pressure. Even when the noncondensable gas is not present, the use of pressure as one of the unknowns appears to be desirable.The procedure developed by Faust and Mercer uses the same unknowns used here, namely pressure and mixture enthalpy, but their procedure for solving the finite difference equations involved requires some modification to allow the introduction of the extra unknown arising from the presence of a noncondensable gas. The numerical methods used by Mercer and Faust, Thomas, and Coats all are based on the earlier work of Price and Coats. Basically the problem involves implicit nonlinear finite difference approximations of the governing partial differential equations that are solved using the partial differential equations that are solved using the Newton-Raphson method. For multidimensional problems the matrices that arise in the problems the matrices that arise in the Newton-Raphson procedure are sparse but have a large bandwidth. Careful ordering of the equations enables the bandwidth to be reduced significantly. Still greater numerical efficiency is possible by using the alternating direction procedure combined with the lagging of corrections to the permeability terms in the Newton-Raphson process, The application of this ADI procedure to petroleum reservoir problems is restricted severely by petroleum reservoir problems is restricted severely by stability limits on the time step, but compressibility and thermal expansion effects in geothermal problems tend to stabilize the scheme. problems tend to stabilize the scheme. JPT P. 52

Double-Mode Energy Management for Multi-Energy System via Distributed Dynamic Event-Triggered Newton-Raphson Algorithm

2020 ◽  
Vol 11 (6) ◽  
pp. 5339-5356 ◽  
Author(s):  
Yushuai Li ◽  
David Wenzhong Gao ◽  
Wei Gao ◽  
Huaguang Zhang ◽  
Jianguo Zhou
Keyword(s):  
Energy Management ◽  
Energy System ◽  
Dynamic Event ◽  
Newton Raphson ◽  
Mode Energy ◽  
Event Triggered ◽  
Raphson Algorithm

scholarly journals Blended Root Finding Algorithm Outperforms Bisection and Regula Falsi Algorithms

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1118
Author(s):  
Sabharwal
Keyword(s):  
Computational Complexity ◽  
Empirical Evidence ◽  
Analytic Solution ◽  
Fundamental Problem ◽  
Numerical Techniques ◽  
Physical Sciences ◽  
Root Finding ◽  
Numerical Computing ◽  
Newton Raphson ◽  
Raphson Algorithm

Finding the roots of an equation is a fundamental problem in various fields, including numerical computing, social and physical sciences. Numerical techniques are used when an analytic solution is not available. There is not a single algorithm that works best for every function. We designed and implemented a new algorithm that is a dynamic blend of the bisection and regula falsi algorithms. The implementation results validate that the new algorithm outperforms both bisection and regula falsi algorithms. It is also observed that the new algorithm outperforms the secant algorithm and the Newton–Raphson algorithm because the new algorithm requires fewer computational iterations and is guaranteed to find a root. The theoretical and empirical evidence shows that the average computational complexity of the new algorithm is considerably less than that of the classical algorithms.

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