POINT BOUNDARY VALUE DIFFERENTIAL EQUATIONS AND NUMERICAL INSTABILITY PROBLEMS

in Theorem 3.1 , so, we do not need to suppose that G t, s is nonnegative.
Remark 3.3. The function f in Theorem 3.1 is not monotone or convex; the conclusions and the proof used in this paper are di ff erent from the known papers in essence.
Proof. It is easy to see that, for any t ∈ J[r]

VALUE PROBLEM ON A TIME SCALE
BASANT KARNA AND BONITA A. LAWRENCE
Received 31 January 2006; Revised 15 April 2006; Accepted 19 April 2006
We will expand the scope of application of a fixed point theorem due to Krasnosel’ski˘ı and Zabreiko to the family of second-o[r]

Finite Element Method - The time dimension - Semi - Discretization of field and dynanic problems analytical solution procedures_17
The description of the laws of physics for space- and time-dependent problems are usually expressed in terms of partial differential equations (PDEs). For the vast maj[r]

Finite Element Method - Steady - state field problems - heat condution, electric and magnetic potential, fluid flow, etc_07
The description of the laws of physics for space- and time-dependent problems are usually expressed in terms of partial differential equations (PDEs). For the vast majority o[r]

Autonomous nonlinear differential equations constituted a system of ordinary differential equations, which often applied in different areas of mechanics, quantum physics, chemical engineering science, physical science, and applied mathematics. It is assumed that the secondorder autonomous nonlinear[r]

problems,” Applicable Analysis, vol. 81, no. 2, pp. 227–240, 2002.
[5] R. Ma, “Multiple positive solutions for a semipositone fourth-order boundary value problem,”
Hiroshima Mathematical Journal, vol. 33, no. 2, pp. 217–227, 2003.
[6] P. J. Y. Wong and R. P. Agarwal[r]

Finite Element Method - Point - Based approximations - Element - free glaerkin - and other meshlees methords_16
The description of the laws of physics for space- and time-dependent problems are usually expressed in terms of partial differential equations (PDEs). For the vast majority of geometries[r]

problems with integral boundary conditions constitute a very interesting and important class of problems. They include two-point, three-point, multipoint and nonlocal boundary value problems as special cases [[21-24], and[r]

6 D. Anderson, R. Avery, and J. Henderson, “Existence of solutions for a one dimensional p -Laplacian
on time-scales,” Journal of Di ff erence Equations and Applications, vol. 10, no. 10, pp. 889–896, 2004.
7 F. M. Atici and G. Sh. Guseinov, “On Green’s functions <[r]

method to get through the first little bit and then reading off “initial” values for
further numerical integration. However it is usually not feasible to integrate into
a singular point, if only because one has not usually expended the same analytic effort to obtain expansio[r]

12 S. Yakubov, Completeness of Root Functions of Regular Di ff erential Operators, vol. 71 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK, 1994.
13 S. Yakubov, “A nonlocal boundary value problem for ellipt[r]

The crucial distinction between initial value problems Chapter 16 and two point boundary value problems this chapter is that in the former case we are able to start an acceptable solutio[r]

must also hold; the primes denote the derivatives with respect to x .
14.4.3. Problems for Hyperbolic Equations: Final Stage of Solution
14.4.3-1. Series solution of boundary value problems for hyperbolic equations.
For hyperbolic equations, the[r]

four-point boundary value problems,” Mathematical and Computer Modelling, vol. 50, no. 9-10, pp.
1348–1359, 2009.
31 Y.-K. Chang, J. J. Nieto, and W.-S. Li, “On impulsive hyperbolic di ff erential inclusions with nonlocal
initial conditions,” Journal o[r]

Figure 17.6.1. FDE matrix structure with an internal boundary condition. The internal condition introduces a special block. (a) Original form, compare with Figure 17.3.1; (b) final form, compare with Figure 17.3.2.
However, the ODEs do have well-behaved derivatives and solutions in t[r]

This paper presents an efficient and accurate numerical technique based upon the scaled boundary finite element method for the analysis of two-dimensional, linear, second-order, boundary value problems with the domain completely described by a circular defining curve. The scaled boundary finite elem[r]

from ordinary di ff erence equations. Here this condition connects the history u 0 with the single
u η . This is suggested by the well-posedness of BVP 1.9 , since the function f depends on the term u t i.e., past values of u .
As usual, a sequence { u − τ , . . . , u T 1 } is s[r]

dq/dx to be proportional to. The problem is that we do not know the proportionality constant. That is, the formula that we might invent would not have the correct integral over the whole range of x so as to make q vary from 1 to M , according to its definition. To solve this problem we introduce a s[r]

k indicates the current mesh point, or block number. k1,k2 label the first and last point in the mesh. If k = k1 or k > k2 , the block involves the boundary conditions at the first or final points; otherwise the block acts on FDEs coupling variables at points k-1 , k .[r]

The_N_ conditions that must be satisfied are that there be agreement in_N_ COMPONENTS OF Y AT_xf_ between the values obtained integrating from one side and from the other, TRANG 2 17.2 S[r]