New Algorithm for Solution of the Non-Linear Equation Systems Occurring in the Design of Thermal Systems

1993 ◽  
Author(s):  
Halil Ibrahim Saraç ◽  
Hasan Riza Güven ◽  
Nedim Sözbir ◽  
Ünal Uysal
Keyword(s):  
Linear Equation ◽  
Linear Systems ◽  
Linear Equations ◽  
Thermal Systems ◽  
Seidel Method ◽  
Non Linear Equation ◽  
Non Linear ◽  
Air Compression ◽  
Non Linear Equations ◽  
Linear Equation Systems

Abstract Models used for the design of thermal systems often lead to non-linear equations which can be converted to linear systems. In this paper, a new algorithm is described for the solution of linear equation systems which have normal or ill-conditioned form A new algorithm and the Gauss-Seidel method were used for two-stage air compression with an inter-cooler. The solutions obtained by using two different methods are compared.

scholarly journals Fuzzy Version of Secant Method to Solve Fuzzy Non-Linear Equations

2016 ◽  
Vol 35 ◽  
pp. 127-134
Author(s):  
Goutam Kumar Saha ◽  
Shapla Shirin
Keyword(s):  
Linear Equation ◽  
Linear Equations ◽  
Approximate Solutions ◽  
Secant Method ◽  
Graphical Representations ◽  
Non Linear Equation ◽  
Non Linear ◽  
Optimum Solution ◽  
Non Linear Equations

In this paper fuzzy version of secant method has been introduced to obtain approximate solutions of a fuzzy non-linear equation. Graphical representations of the approximate solutions have also been shown. The idea of converging to the root to the desired degree of accuracy, which is the optimum solution, of a fuzzy non-linear equation has been focused.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 127-134

scholarly journals The Non-Linear Equations for the Green Function and Calculation of the Magnetic Field Turbulent Diffusivities and α-Effect

1993 ◽  
Vol 157 ◽  
pp. 245-248
Author(s):  
N.A. Silant'ev
Keyword(s):  
Green Function ◽  
Linear Equation ◽  
Linear Equations ◽  
Characteristic Parameter ◽  
Turbulent Medium ◽  
Non Linear Equation ◽  
Non Linear ◽  
The Green Function ◽  
The Magnetic Field ◽  
Non Linear Equations

The exact numerical solution of the simplest non-linear equation from the hierarchy of non-linear equations for the averaged Green function shows that such solution allows to calculate the diffusivity and α-effect coefficient with a good accuracy for an arbitrary spectra of turbulence for all values of the characteristic parameter. It is derived also the improved equation describing the evolution of admixture fluctuations in a turbulent medium which takes into account the non-linear equation for the averaged Green function.

scholarly journals Performance Assessment Techniques for the 3-Phase IAG

2019 ◽  
Vol 9 (2) ◽  
pp. 2191-2200
Keyword(s):  
Performance Assessment ◽  
Linear Equations ◽  
Optimization Technique ◽  
Advantages And Disadvantages ◽  
Non Linear Equation ◽  
Non Linear ◽  
Assessment Techniques ◽  
Preliminary Study ◽  
Non Linear Equations ◽  
Steady State Performance

This manuscript covers the analytical and optimization based techniques for the performance assessment of 3-phase IAG furnishing 3-phase and 1-phase load. It examines initially the basic phenomenon of voltage build-up and then the steady state performance of 3-phase IAG furnishing 3-phase and 1-phase load. This preliminary study forms the foundation or basis of the design of future controllers. The conventional techniques and MATLAB based optimization technique fsolve is elaborated in detail along-with advantages and disadvantages for attaining the solution of simultaneous non linear equation. The fsolve technique is recommended for the solution of non-linear equations due to its advantages over conventional method.

Complementary bounds for inner products associated with non-linear equations

1984 ◽  
Vol 96 (1-2) ◽  
pp. 135-142 ◽  
Author(s):  
R. J. Cole ◽  
J. Mika ◽  
D. C. Pack
Keyword(s):  
Real Hilbert Space ◽  
Linear Equations ◽  
Linear Operators ◽  
Inner Product ◽  
Upper And Lower Bounds ◽  
Non Linear Equation ◽  
Non Linear ◽  
Non Linear Operator ◽  
Non Linear Equations ◽  
Unknown Solution

SynopsisFunctionals are found that give upper and lower bounds to the inner product 〈g0, f〉 involving the unknown solution f of a non-linear equation T[f] = f0, with f∈H, a real Hilbert space, g0 a given function in H and f0 a given function in the range of the non-linear operator T. The method depends upon a re-ordering of terms in the expansion of T[f] about a trial function so as to transfer the non-linearity to a secondary problem that requires its own particular treatment and to enable earlier results obtained for linear operators to be used for the main part. First, bivariational bounds due to Barnsley and Robinson are re-derived. The new and more accurate bounds are given under relaxed assumptions on the operator T by introducing a third approximating function. The results are obtained from identities, thus avoiding some of the conditions imposed by the use of variational methods. The accuracy of the new method is illustrated by applying it to the problem of the heat contained in a bar.

scholarly journals A New Approach To Solve Fuzzy Non-Linear Equations Using Fixed Point Iteration Algorithm

2013 ◽  
Vol 32 ◽  
pp. 15-21
Author(s):  
Goutam Kumar Saha ◽  
Shapla Shirin
Keyword(s):  
Fixed Point ◽  
Linear Equation ◽  
Graphical Representation ◽  
Linear Equations ◽  
Approximate Solutions ◽  
Iteration Algorithm ◽  
Fixed Point Iteration ◽  
New Approach ◽  
Non Linear Equation ◽  
Non Linear

A non-linear equation over linear fuzzy real numbers is called a fuzzy non-linear  equation. In Classical Mathematics a non-linear equation can be solved by using  different types of numerical methods. In this paper a new approach has been  introduced to get approximate solutions with the help of Fixed Point Iteration  Algorithm. Graphical representation of the solutions has also been drawn so that  anyone can achieve the idea of converging to the root of a fuzzy non-linear equation. DOI: http://dx.doi.org/10.3329/ganit.v32i0.13641 GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 32 (2012) 15 – 21

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