nonlinear system of equations solver

... America). Chapter 9. Root Finding and Nonlinear Sets of Equations 9.0 Introduction We now consider that most basic of tasks, solving equations numerically. While most equations are born with both a ... (in this context) gives us the hope of satisfying N equations in N unknowns simultaneously. Note that we have only hope, not certainty. A nonlinear set of equations may have no (real) solutions ... are the individual equations to be satisfied simultaneously. Don’t be fooled by the apparent notational similarity of equations (9.0.2) and (9.0.1). Simultaneous solution of equations in N dimensions...

Ngày tải lên: 07/11/2013, 19:15

... 352 Chapter 9. Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... event, with 2 −40 ≈ 10 −12 . 354 Chapter 9. Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... iteration one of the previous boundary points is discarded in favor of the latest estimate of the root. The only difference between the methods is that secant retains the most recent of the prior...

Ngày tải lên: 15/12/2013, 04:15

... York: McGraw-Hill), Đ 8.3. Ostrowski, A.M. 1966, Solutions of Equations and Systems of Equations , 2nd ed. (New York: Academic Press), Chapter 12. Ridders, C.J.F. 1979, IEEE Transactions on Circuits and Systems , vol. CAS-26, pp. ... converge: Local behavior might send it off towards infinity. 356 Chapter 9. Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... number of iterations exceeded in rtsec"); return 0.0; Never get here. } 358 Chapter 9. Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...

Ngày tải lên: 15/12/2013, 04:15

... York: McGraw-Hill), Đ 8.3. Ostrowski, A.M. 1966, Solutions of Equations and Systems of Equations , 2nd ed. (New York: Academic Press), Chapter 12. Ridders, C.J.F. 1979, IEEE Transactions on Circuits and Systems , vol. CAS-26, pp. ... superlinear convergence with the sureness of bisection? 360 Chapter 9. Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... 362 Chapter 9. Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C)...

Ngày tải lên: 15/12/2013, 04:15

... 366 Chapter 9. Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... evaluation per iteration. 368 Chapter 9. Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) ... is the set of points from which Newton’s method convergesto the root z = 1of the equation z 3 − 1=0. Its shape is fractal. of the desired root. But that means that in the neighborhood of an extremum...

Ngày tải lên: 15/12/2013, 04:15

... Newton-Raphson Method for Nonlinear Systems of Equations We make an extreme, but wholly defensible, statement: There are no good, gen- eral methods for solving systems of more than one nonlinear equation. ... as P  j (x)= P  (x) (x−x 1 )···(x−x j ) − P(x) (x−x 1 )···(x−x j ) j  i=1 (x − x i ) −1 (9.5.28) 9.6 Newton-Raphson Method for Nonlinear Systems of Equations 379 Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... f’s point of view, or from g’s. In order to find all common points, which are 372 Chapter 9. Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...

Ngày tải lên: 15/12/2013, 04:15

... vector of values x i and F denote the entire vector of functions F i . In the neighborhood of x, each of the functions F i can be expanded 9.6 Newton-Raphson Method for Nonlinear Systems of Equations 379 Sample ... Solution of Nonlinear Equations in Several Vari- ables (New York: Academic Press). 9.7 Globally Convergent Methods for Nonlinear Systems of Equations We have seen that Newton’s method for solving nonlinear ... Newton-Raphson Method for Nonlinear Systems of Equations We make an extreme, but wholly defensible, statement: There are no good, gen- eral methods for solving systems of more than one nonlinear equation....

Ngày tải lên: 15/12/2013, 04:15

... Solution of Nonlinear Equations in Several Vari- ables (New York: Academic Press). 9.7 Globally Convergent Methods for Nonlinear Systems of Equations We have seen that Newton’s method for solving nonlinear ... corrected edition (Washington: Mathe- matical Association of America), Chapter 14. [1] Ostrowski, A.M. 1966, Solutions of Equations and Systems of Equations , 2nd ed. (New York: Academic Press). Ortega, ... rate of decrease of f.(Forexamplesof such sequences, see [1] , p. 117.) A simple way to fix the first problem is to require the average rate of decrease of f to be at least some fraction α of the...

Ngày tải lên: 15/12/2013, 04:15

... decay of solutions for a quaslinear system of viscoelastic equations. Nonlinear Anal. 71, 2257–2267 (2009). doi:10.1016/j.na.2009.01.060 22. Agre, K, Rammaha, MA: Systems of nonlinear wave equations ... (2006) 23. Said-Houari, B, Messaoudi, SA, Guesmia, A: General decay of solutions of a nonlinear system of viscoelastic wave equations. Nonlinear Diff. Equ. Appl. (2011) 24. Muñoz Rivera, JE: Global ... doi:10.1002/mma.340 19. Han, XS, Wang, WM: Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source. Nonlinear Anal. 71, 5427–5450 (2009). doi:10.1016/j.na.2009.04.031 20....

Ngày tải lên: 21/06/2014, 00:20

... uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations. Fixed Point Theory Appl 2010, 2010:1-17. 30. Babakhani A: Positive solutions for system of nonlinear ... of author information is available at the end of the article Abstract In this article, we study the existence of positive solutions for a coupled system of nonlinear differential equ ations of ... problems of N-Dimension nonlinear fractional differential system. Bound Value Probl 2008, 2008:1-15. 24. Bai C, Fang J: The existence of a positive solution for a singular coupled system of nonlinear...

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... stability of a second-order system of difference equations. Discrete Dyn Nat Soc 2008, 12 (2008). (Article ID 860152) 11. Irićanin, B, Stević, S: Some systems of nonlinear difference equations of higher ... behavior of a three-dimensional linear fractional system of difference equations. J Math Anal Appl. 310, 673–689 (2005) 8. Özban, AY: On the positive solutions of the system of rational difference equations x n+1 = 1 y n−k , y n+1 = y n x n−m y n−m−k . . ... r of solutions of the system of difference equations x n+1 = a + x n b + y n , y n+1 = c + y n d + z n , z n+1 = e + z n f + x n . In [8], Özban studied the positive solutions of the system of...

Ngày tải lên: 20/06/2014, 22:20

... nonnegative numbers. System (1) was mentioned in [1] as one of three systems of Open Problem 3, which asked for a description of the global dynamics of some rational systems of difference equations. In ... then the interior of 〚u 1 ,u 2 〛 is either a subset of the basin of attraction of u 1 or a subset of the basin of attraction of u 2 . Kalabušić et al. Advances in Difference Equations 2011, 2011:29 http://www.advancesindifferenceequations.com/content/2011/1/29 Page ... inequality 1.i) of Lemma 1, then the proof of Theorem is similar to the proof of parts (ℛ 9 )and(ℛ 10 ). This completes the proof of Theorem in the regions ℛ 12 , ℛ 13 .Thisisanexampleof semistable...

Ngày tải lên: 21/06/2014, 00:20

... uniqueness of the solutions are obtained. Keywords: systems of elliptic equations, degenerate elliptic equations, boundary value problems, Dirichlet type problem 1 Introduction and statement of the ... stasys. rutkauskas@mii.vu.lt Institute of Mathematics and Informatics of Vilnius University, Akademijos str. 4, LT-08863, Vilnius, Lithuania Abstract A system of elliptic equations which are irregularly ... 2011:16 http://www.boundaryvalueproblems.com/content/2011/1/16 Page 5 of 11 RESEARC H Open Access On the solvability conditions of the first boundary value problem for a system of elliptic equations that strongly degenerate at...

Ngày tải lên: 21/06/2014, 00:20

... in Difference Equations 2011, 2011:14 http://www.advancesindifferenceequations.com/content/2011/1/14 Page 10 of 17 It completes the proof. Now consider the existence of solutions of PBVP (1.1). ... functio n r(t)=-||x (t)|| 2 , t Î [0, 1], where x(t) is a soluti on of (3.6), for the rest part of the proof we proceed as in the proof of Theorem 3.1. Corollary 3.2 Let f be a scalar-valued function ... integro-differential equation of Volterra type on time scales. Nonlinear Anal. 60, 429–442 (2005) 15. Xing, Y, Ding, W, Han, M: Periodic boundary value problems of integro-differential equations of Volterra type...

Ngày tải lên: 21/06/2014, 02:20

... argument θ of the complex root is a rational multiple of π, the system is globally periodic. 4.4. Stability of Fixed Points We finish this section with the complete study of the stability of the fixed ... some of those systems can be reduced to some Ricatti equations or to some previously studied second-order rational equations. Further, since, for some choices of the parameters, one obtains a system which ... attention on three aspects of the dynamics of the system: the boundedness character and asymptotic behavior of its solutions, the existence of periodic orbits in particular, of prime period-two solutions,...

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