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Solving Variable-Coefficient Fourth-Order ODEs with Polynomial Nonlinearity by Symmetric Homotopy Method

2018
*
Applied and Computational Mathematics
*

*The*symmetry

*of*

*the*

*solution*set for

*the*resulting

*system*

*of*

*polynomial*equations obtained from EEM

*of*

*the*problem is analyzed. ...

*The*symmetric homotopy method is constructed to calculate all

*solutions*

*of*

*the*discretization

*system*for

*the*problem. Due to

*the*exploitation

*of*symmetry,

*the*number

*of*

*computations*is reduced. ... Acknowledgements This work is supported in part by

*the*National Natural Science Foundation

*of*China (11571061, 11401075) and in part by

*the*Fundamental Research Funds for

*the*Central Universities (DUT16LK36 ...

##
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Page 5411 of Mathematical Reviews Vol. , Issue 88j
[page]

1988
*
Mathematical Reviews
*

An upper bound on

*the*number*of*isolated*solutions**of**the**system*(Bezout number) is*the*product d*of**the*degrees*of**the**polynomials*. ... This is a review paper on algorithms for*the*inclusion*of**solutions*to*nonlinear**systems**of*equations, based on interval arithmetic tools. ...##
###
On the diagonal approximation of full matrices

1996
*
Journal of Computational and Applied Mathematics
*

*The*matrices are constructed using

*the*well-known

*computer*algebra

*system*Maple.

*The*techniques we show are applicable to square matrices in general. ... In this paper

*the*construction

*of*diagonal matrices, in some sense approximating

*the*inverse

*of*a given square matrix, is described. ... Sommeijer for introducing me to

*the*problem

*of*

*the*construction

*of*diagonal matrices. I also want to acknowledge Dr. B.P. Sommeijer for his valuable comments during

*the*preparation

*of*this paper. ...

##
###
Some computational methods for systems of nonlinear equations and systems of polynomial equations

1992
*
Journal of Global Optimization
*

This paper gives a brief survey and assessment

doi:10.1007/bf00122427
fatcat:fycqststzjdhjk6vxzgflx463a
*of**computational*methods for finding*solutions*to*systems**of**nonlinear*equations and*systems**of**polynomial*equations. ...*Systems**of**nonlinear*equations,*systems**of**polynomial*equations, simplicial algorithms, pivoting algorithms, homotopy algorithms, Kuhn's method for finding roots*of*a*polynomial*, Nielsen fixed point theory ... We will show how*the*additional problem*of*having more than one*solution*to*systems**of**nonlinear*equations has mobilized*the*imagination*of*researchers. ...##
###
Approximate Bisimulation and Optimization of Software Programs Based on Symbolic-Numeric Computation

2013
*
Mathematical Problems in Engineering
*

Then,

doi:10.1155/2013/421926
fatcat:i3atxugbt5fx3nlkz5g6xynpoe
*the*notion*of*bisimulation for software programs is proposed based on*the*equivalence relation*of*corresponding*nonlinear**polynomial**systems*in their*nonlinear**polynomial*transition*systems*. ... called a*nonlinear**polynomial*transition*system*to represent*the*behavior and structure*of**the*software program. ...*of**the**nonlinear**polynomial**systems*. ...##
###
Page 5702 of Mathematical Reviews Vol. , Issue 92j
[page]

1992
*
Mathematical Reviews
*

It describes, in detail and by a lot

*of*examples, some strategies to avoid inflationary effects*of**the**computed*sets for*the**solution**of**nonlinear**systems*. ... (English summary) [Numerical calculation*of**the*isolated*solutions**of*a*polynomial**system**of*several complex variables] RAIRO Rech. Opér. 25 (1991), no. 3, 277-289. ...##
###
Polynomial Least Squares Method for the Solution of Nonlinear Volterra-Fredholm Integral Equations

2014
*
Mathematical Problems in Engineering
*

*The*present paper presents

*the*application

*of*

*the*

*polynomial*least squares method to

*nonlinear*integral equations

*of*

*the*mixed Volterra-Fredholm type. ... For this type

*of*equations, accurate approximate

*polynomial*

*solutions*are obtained in a straightforward manner and numerical examples are given to illustrate

*the*validity and

*the*applicability

*of*

*the*method ... Conflict

*of*Interests

*The*authors declare that there is no conflict

*of*interests regarding

*the*publication

*of*this paper. ...

##
###
Page 4516 of Mathematical Reviews Vol. , Issue 93h
[page]

1993
*
Mathematical Reviews
*

A

*nonlinear*homotopy method for*the*numerical determination*of*all isolated*solutions**of*deficient*polynomial**systems**of**the*form P(q,x) =0 is introduced, where q € C° is a set*of*parameters. ... Anal. 19 (1982), no. 2, 400-408; MR 83b:65056] to*the**solution**of**systems**of**nonlinear*algebraic equations is ana- lyzed. ...##
###
Page 3202 of Mathematical Reviews Vol. , Issue 97E
[page]

1997
*
Mathematical Reviews
*

A new algorithm for solving

*systems**of**nonlinear**polynomial*equations is presented. ... These schemas are applied to*the**solution**of**systems**of*equations. ...##
###
Page 479 of Mathematical Reviews Vol. , Issue 2004a
[page]

2004
*
Mathematical Reviews
*

Summary: “

*The*focus*of*this paper is on*the*numerical solu- tion*of*large sparse*nonlinear**systems**of*algebraic equations on parallel*computers*. ... Summary: “*The*pseudozero set*of*a*system*f*of**polynomials*in n complex variables is*the*subset*of*C” which is*the*union*of**the*zero-sets*of*all*polynomial**systems*g that are near to f in a suitable sense ...##
###
Analytic solution of GPS atmospheric sounding refraction angles

2004
*
Earth, Planets and Space
*

*of*

*the*

*solution*space. ...

*The*Newton's iterative method is often used owing to

*the*bottleneck

*of*solving in exact form

*the*

*nonlinear*

*system*

*of*equations for bending angles. ...

*The*first author wishes to acknowledge

*the*support

*of*JSPS (Japan Society

*of*Promotion

*of*Science) for

*the*financial support that enabled

*the*undertaking

*of*this study at

*the*Department

*of*Geophysics, ...

##
###
Numerical Solutions of System of Second Order Boundary Value Problems using Galerkin Method

2018
*
GANIT Journal of Bangladesh Mathematical Society
*

<p>In this paper we derive

doi:10.3329/ganit.v37i0.35734
fatcat:lkmfk5pwvneplgj3ocf5f7fyuy
*the*formulation*of*one dimensional linear and*nonlinear**system**of*second order boundary value problems (BVPs) for*the*pair*of*functions using Galerkin weighted residual method ... Finally,*the*approximate*solutions*are compared with*the*exact*solutions*and also with*the**solutions**of**the*existing methods.</p><p>GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 161-174</p> ... For a*nonlinear**system**of*second order BVPs [3] , there are few valid methods to obtain*the*numerical*solutions*. ...##
###
Approximate Analytical Solutions of the Fractional-Order Brusselator System Using the Polynomial Least Squares Method

2015
*
Advances in Mathematical Physics
*

PLSM allows us to

doi:10.1155/2015/450235
fatcat:nymtlirprrbg3gketkiyqyf6jy
*compute*approximate analytical*solutions*for*the*Brusselator*system*, which is a fractional-order*system**of**nonlinear*differential equations. ...*The*paper presents a new method, called*the**Polynomial*Least Squares Method (PLSM). ... Conflict*of*Interests*The*authors declare that there is no conflict*of*interests regarding*the*publication*of*this paper. ...##
###
Page 3923 of Mathematical Reviews Vol. , Issue 91G
[page]

1991
*
Mathematical Reviews
*

(H-AGUG) Block ABS methods for

*nonlinear**systems**of*algebraic equations.*Computational**solution**of**nonlinear**systems**of*equations (Fort Collins, CO, 1988), 181-187, Lectures in Appl. Math., 26, Amer. ... (i-NDM) Generically nonsingular*polynomial*continuation.*Computational**solution**of**nonlinear**systems**of*equations (Fort Collins, CO, 1988), 467-493, Lectures in Appl. Math., 26, Amer. Math. ...##
###
Bezier Polynomials with Applications

2018
*
Dhaka University Journal of Science
*

A rigorous matrix formulation is developed by

doi:10.3329/dujs.v66i2.54562
fatcat:xhbnbog6jzhm7c4bgiia53wvcq
*the*Galerkin method for linear and*nonlinear**systems*and solved it using Bezier*polynomials*. ...*The*approximate*solutions*are compared to*the*exact*solutions*through tabular form. All problems are*computed*using*the*software MATHEMATICA. Dhaka Univ. J. Sci. 66(2): 157-162, 2018 (July) ... during*the*period*of*research work. ...
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