point boundary value differential equations and numerical instability problems

... p-Laplacian boundary value problems with advanced arguments Appl Math Comput 2009, 215:125-131 Jankowski T: Solvability of three point boundary value problems for second order differential equations ... some three point boundary value problems via fixed point index theory Nonlinear Anal 2001, 47:4319-4332 Raffoul YN: Positive solutions of three -point nonlinear second order boundary value problem ... three -point boundary value problem J Math Anal Appl 1994, 183:518-522 Feng W, Webb JRL: Solvability of three point boundary value problems at resonance Nonlinear Anal 1997, 30(6):3227-3238 Anderson...

Ngày tải lên: 21/06/2014, 03:20

... two -point singular boundary value problems, [6] Functional Differential Equations 10 (2003), no 1-2, 259–281, Functional differential equations and applications (Beer-Sheva, 2002) , On two -point boundary ... Agarwal, Focal boundary value problems for differential and difference equations, Mathematics and Its Applications, vol 436, Kluwer Academic Publishers, Dordrecht, 1998 [2] R P Agarwal and D O’Regan, ... multi -point boundary value problem, Annali di Matematica Pura ed Ap[4] plicata Series IV 86 (1970), 367–399 [5] I Kiguradze, Some singular boundary value problems for ordinary differential equations, ...

Ngày tải lên: 23/06/2014, 00:20

... to boundary value problems on time scales,” Advances in Difference Equations, vol 2004, no 2, pp 93–109, 2004 12 C C Tisdell and H B Thompson, “On the existence of solutions to boundary value problems ... Y N Raffoul, and C C Tisdell, “Three point boundary value problems on time scales,” Journal of Difference Equations and Applications, vol 10, no 9, pp 843–849, 2004 22 R E Bellman and R E Kalaba, ... Journal of Differential Equations, vol 2003, no 82, pp 1–11, 2003 16 R A Khan, J J Nieto, and V Otero-Espinar, “Existence and approximation of solution of three -point boundary value problems on time...

Ngày tải lên: 21/06/2014, 16:20

... Multi -point boundary value problems for an increasing homeomorphism and positive homomorphism on time scales Liu Yang∗1,2 and Weiguo Zhang1 College of Science, University of Shanghai for Science and ... increasing homeomorphism and positive homomorphism 1 Introduction With the development of boundary value problems for differential equations [1–5], dif- ference equations [6, 7], and the theory of time ... for nonlinear m -point boundary value problem J Math Anal Appl 256, 556–567 (2001) [3] Bai, Z, Ge, W, Wang, Y: Multiplicity results for some second-order four -point boundary- value problems Nonlinear...

Ngày tải lên: 21/06/2014, 17:20

... 2 Boundary Value Problems Multipoint boundary value problems for second-order ordinary differential equations arise in many areas of applied mathematics and physics; see 1–3 and references ... Mathematics and Computation, vol 198, no 2, pp 487–493, 2008 X Du and Z Zhao, “Existence and uniqueness of positive solutions to a class of singular m -point boundary value problems, ” Boundary Value Problems, ... three -point boundary value problems for nonlinear second-order ordinary differential equations was initiated by Lomtatidze 4, Since then, the nonlinear secondorder multipoint boundary value problems...

Ngày tải lên: 21/06/2014, 18:20

... Multi -point boundary value problems for an increasing homeomorphism and positive homomorphism on time scales Liu Yang∗1,2 and Weiguo Zhang1 College of Science, University of Shanghai for Science and ... increasing homeomorphism and positive homomorphism 1 Introduction With the development of boundary value problems for differential equations [1–5], dif- ference equations [6, 7], and the theory of time ... for nonlinear m -point boundary value problem J Math Anal Appl 256, 556–567 (2001) [3] Bai, Z, Ge, W, Wang, Y: Multiplicity results for some second-order four -point boundary- value problems Nonlinear...

Ngày tải lên: 21/06/2014, 20:20

... rare Boundary Value Problems up to now In this paper, we will study the existence and uniqueness of smooth positive solutions to the second-order singular m -point boundary value problem 1.1 and ... superlinear m -point boundary value problems, ” Applied Mathematics and Computation, vol 179, no 1, pp 67–78, 2006 Y Zhang, “Positive solutions of singular sublinear Emden-Fowler boundary value problems, ” ... then a necessary and sufficient condition for the problem 1.1 and 4.6 to have smooth positive solution is that 0< f s, s, s ds < ∞ 4.8 Boundary Value Problems 13 Theorem 4.6 Suppose H and 4.8 hold,...

Ngày tải lên: 21/06/2014, 20:20

... Gupta, and J.-M Xu, “Existence and uniqueness theorems for three -point boundary value problems, ” SIAM Journal on Mathematical Analysis, vol 20, no 3, pp 716–726, 1989 R P Agarwal, Boundary Value Problems ... focal eigenvalue problem,” Boundary Value Problems, vol 2007, Article ID 23108, 12 pages, 2007 15 V R G Moorti and J B Garner, “Existence-uniqueness theorems for three -point boundary value problems ... Mathematical Analysis and Applications, vol 327, no 1, pp 23–35, 2007 18 Y Shi and M Pei, “Two -point and three -point boundary value problems for nth-order nonlinear differential equations, ” Applicable...

Ngày tải lên: 21/06/2014, 20:20

... Two Point Boundary Value Problems desired boundary value required boundary value x Figure 17.0.1 Shooting method (schematic) Trial integrations that satisfy the boundary condition at one endpoint ... 756 Chapter 17 Two Point Boundary Value Problems Problems Reducible to the Standard Boundary Problem dyi (x) = gi (x, y1 , , yN , λ) dx (17.0.4) and one has to satisfy N + boundary conditions ... important problems that can be reduced to the standard boundary value problem described by equations (17.0.1) – (17.0.3) The first is the eigenvalue problem for differential equations Here the right-hand...

Ngày tải lên: 24/12/2013, 12:16

... 758 Chapter 17 Two Point Boundary Value Problems Now, as far as Newton-Raphson is concerned, we are nearly in business We want to find a vector value of V that zeros the vector value of F We this ... mismatch, and n2 for the partial derivatives Each new cycle requires a new round of n2 + integrations This illustrates the enormous extra effort involved in solving two point boundary value problems ... odeint(y,nvar,x1,x2,EPS,h1,hmin,&nok,&nbad,derivs,rkqs); score(x2,y,f); free_vector(y,1,nvar); 760 Chapter 17 Two Point Boundary Value Problems 17.2 Shooting to a Fitting Point yi (x1 ) = yi (x1 ; V(1)1 , , V(1)n2 ) i = 1, , N (17.2.1)...

Ngày tải lên: 24/12/2013, 12:16

... f[]) Routine for use with newt to solve a two point boundary value problem for nvar coupled ODEs by shooting from x1 and x2 to a fitting point xf Initial values for the nvar ODEs at x1 (x2) are generated ... Acton, F.S 1970, Numerical Methods That Work; 1990, corrected edition (Washington: Mathematical Association of America) Keller, H.B 1968, Numerical Methods for Two -Point Boundary- Value Problems (Waltham, ... are boundary value problems where even shooting to a fitting point fails — the integration interval has to be partitioned by several fitting points with the solution being matched at each such point...

Ngày tải lên: 24/12/2013, 12:16

... total of (M − 1)N equations for the M N unknowns The remaining N equations come from the boundary conditions At the first boundary we have 764 Chapter 17 Two Point Boundary Value Problems where Sj,n ... only points k, k − Figure 17.3.1 illustrates the typical structure of the complete matrix equation for the case of variables and mesh points, with boundary conditions at the first boundary and ... left-hand corner of the matrix comes from the boundary condition Sj,n at point k = The next three × 10 blocks are the Sj,n at the interior points, coupling variables at mesh points (2,1), (3,2), and...

Ngày tải lên: 24/12/2013, 12:16

... 774 Chapter 17 Two Point Boundary Value Problems and similarly for Smn The boundary conditions on (17.4.4) require that y be regular at x = ±1 In other words, near the endpoints the solution ... Chapter 17 Two Point Boundary Value Problems x = −1) Note that the boundary condition is actually applied a distance dx from the boundary to avoid having to evaluate y2 right on the boundary The ... best estimate, v[1] It also sets the boundary values of y1 and y2 using equations (17.4.20) and (17.4.19) (with a minus sign corresponding to Sample page from NUMERICAL RECIPES IN C: THE ART OF...

Ngày tải lên: 21/01/2014, 18:20

... Press), pp 129ff 17.6 Handling Internal Boundary Conditions or Singular Points Singularities can occur in the interiors of two point boundary value problems Typically, there is a point xs at which ... 784 Chapter 17 Two Point Boundary Value Problems where φ(x) is chosen by us Written in terms of the mesh variable q, this equation ... variables that must hold at a point We discussed a related situation earlier, in §17.2, when we described the “fitting point method” to handle the task of integrating equations with singular behavior...

Ngày tải lên: 21/01/2014, 18:20

... Two Point Boundary Value Problems where xs is the unknown location of the singularity, and change the independent variable to t by setting x − x1 = tz, 0≤t≤1 (17.6.4) D(x, y) = (17.6.5) The boundary ... contains equations with boundary conditions at the first point, one “internal” boundary condition, and two final boundary conditions The figure shows the structure of the overall matrix equations along ... derivatives and solutions in the neighborhood of the singularity, so it is readily possible to integrate away from the point Both the relaxation method and the method of “shooting” to a fitting point handle...

Ngày tải lên: 21/01/2014, 18:20

... SMART (eds) Perturbation of the boundary in boundary- value problems of partial differential equations, D HENRY Double affine Hecke algebras, I CHEREDNIK ´ˇ L-functions and Galois representations, ... turbulent boundary- driven flows (Problems I–IV below) The flows admit mixed, non-standard boundary conditions and also time-dependent driving forces (Problems III and IV) We are interested in the ... result 2.2 Formulation of the problem and the results 2.2.1 Balance equations, boundary and initial conditions Structure of S and q c We are interested in understanding the mathematical properties...

Ngày tải lên: 14/03/2014, 10:20

... of linear operators and applications to partial differential equations, Springer-Verlag New York Inc, 1983 [12] K.G Valeev, O.A Raoutukov, Infinite system of differential equations, Scientis ... Levinson’s theorem to the case of linear delay differential equations under nonlinear perturbation (see [1, 13, 14]) Let’s consider the two following differential equations: dx(t) = Ax(t), t ≥ 0, dt (9) ... (see [9], H.Inaba), A : D(A) ⊂ E → E and operator f : R+ × E → E is continuous in t and satisfies all conditions (5), (6), (7) And now, we introduce the delay differential equation: d p(t) = Ap(t)...

Ngày tải lên: 22/03/2014, 11:20

... Differential equations in the complex domain The basic existence and uniqueness result Linear equations The Frobenius method Second order equations 61 61 63 67 70 Chapter §5.1 §5.2 §5.3 §5.4 Boundary value ... linear equations, the Floquet theorem, and the autonomous linear flow Then we establish the Frobenius method for linear equations in the complex domain and investigates Sturm–Liouville type boundary ... some α ∈ C If (3.7) holds, α is called an eigenvalue of A and x is called eigenvector In particular, α is an eigenvalue if and only if Ker(A − α) = {0} and hence Ker(A − α) is called the eigenspace...

Ngày tải lên: 31/03/2014, 15:56

Ngày tải lên: 31/03/2014, 15:56

... integral and differential forms, material properties, constitutive relations, and interface conditions Discussed are potentials and problems formulated in terms of potentials, and the time-domain and ... theory, study of matrices and determinants, boundary value problems for partial differential equations, probability theory, Markov chains, several areas of mathematical physics, and education of mathematics ... Hermite and Argyris elements with application to fourthorder problems rooted in the bending of elastic beams and plates Since the fourth-order problems are less standard than second-order equations, ...

Ngày tải lên: 31/03/2014, 15:57