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

Abdrhaman Mahmoud
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  ... 
doi:10.11648/j.acm.20180702.14 fatcat:fn7xi3tngvfzxn3ynm5fa2ptcm

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

Walter M. Lioen
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.  ... 
doi:10.1016/s0377-0427(96)00054-4 fatcat:3zk7ek4gbjffhnu4uhrpltipoy

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

W. Forster
1992 Journal of Global Optimization  
This paper gives a brief survey and assessment 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.  ... 
doi:10.1007/bf00122427 fatcat:fycqststzjdhjk6vxzgflx463a

Approximate Bisimulation and Optimization of Software Programs Based on Symbolic-Numeric Computation

Hui Deng, Jinzhao Wu
2013 Mathematical Problems in Engineering  
Then, 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.  ... 
doi:10.1155/2013/421926 fatcat:i3atxugbt5fx3nlkz5g6xynpoe

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

Bogdan Căruntu, Constantin Bota
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.  ... 
doi:10.1155/2014/147079 fatcat:vdpf6ctdprdkxflmrtzt6uette

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

Joseph L. Awange, Yoichi Fukuda, Shuzo Takemoto, Jens Wickert, Yuichi Aoyama
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,  ... 
doi:10.1186/bf03352518 fatcat:dccmzze6erfu7ouoprvojtzwxi

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

Mahua Jahan Rupa, Md Shafiqul Islam
2018 GANIT Journal of Bangladesh Mathematical Society  
<p>In this paper we derive 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.  ... 
doi:10.3329/ganit.v37i0.35734 fatcat:lkmfk5pwvneplgj3ocf5f7fyuy

Approximate Analytical Solutions of the Fractional-Order Brusselator System Using the Polynomial Least Squares Method

Constantin Bota, Bogdan Căruntu
2015 Advances in Mathematical Physics  
PLSM allows us to 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.  ... 
doi:10.1155/2015/450235 fatcat:nymtlirprrbg3gketkiyqyf6jy

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

Nazrul Islam, Md Shafiqul Islam
2018 Dhaka University Journal of Science  
A rigorous matrix formulation is developed by 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.  ... 
doi:10.3329/dujs.v66i2.54562 fatcat:xhbnbog6jzhm7c4bgiia53wvcq
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