Abst rac t -An alternative to control of the global error of a numerical solution to a boundary value problem (BVP) for ordinary differential equations (ODEs) is control of its residual, the amount by which it fails to satisfy the ODEs and boundary conditions. Among the methods used by codes tha t control residuals are collocation, Runge-Kut ta methods with continuous extensions, and shooting. ...

It is proved that the solution to exterior Neumann boundary value problem can be obtained as the limit of the solutions of some problems in the whole space. 1 Consider the following problem: (V' + k*)u =f in f2, ul,=O, where f2 = R3\D. D is bounded domain with a smooth boundary r, fE C,(Q), k > 0. In [l] we proved the following: THEOREM 1. Consider the problem V=N in D N = const. > 0. =0 in Q, ...

Previous research (12) showed that connecting the human body to the earth during sleep normalizes circadian cortisol profiles and reduces or eliminates various subjectively reported symptoms, including sleep dysfunction, pain and stress. We therefore hypothesized that earthing might also influence other aspects of physiology. Fifty-eight healthy adult subjects (30 controls) participated in a do...

Consider the higher order nonlinear scalar differential equations (0.1) x(t) = −f(t, x(t), ..., y(t), ...y(2(n−1))(t)), 0 ≤ t ≤ 1 where f ∈ C([0, 1] × R+, R+), R+ = [0,∞) associated to the Lidstone boundary conditions (0.2) x(0) = 0 = x(1), (0.3) x(0) = 0 = x(1). Existence of a solution of boundary value Problems (BVP) (0.1)-(0.2) such that x(t) > 0, 0 < t < 1, i = 0, 1, ..., n− 1 are given, un...

&lt;p style='text-indent:20px;'&gt;We study boundedness of solutions to a linear boundary value problem (BVP) modelling two-layer ocean with uniform eddy viscosity in the lower layer and variable upper layer. We analyse bounds given on examples different profiles case their parameter dependence.&lt;/p&gt;

Background. Previous studies assessing various cytokines in the critically ill/injured have been uninformative in terms of translating to clinical care management. Animal abdominal sepsis work suggests that enhanced intraperitoneal (IP) clearance of Damage-Associated Molecular Patterns (DAMPs) improves outcome. Thus measuring the responses of DAMPs offers alternate potential insights and a repr...

sinc-galerkin method based upon double exponential transformation for solving troesch&apos;s problem was given in this study. properties of the sinc-galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.the error bound of the method was fo...

Hua Su School of Statistics and Mathematic, Shandong University of Finance, Jinan, Shandong 250014, China Correspondence should be addressed to Hua Su, [email protected] Received 24 October 2008; Accepted 31 January 2009 Recommended by Binggen Zhang We study the existence of positive solutions for the following nonlinear m-point boundary value problem for an increasing homeomorphism and homomorph...

In this paper, we are concerned with proving the existence of positive solutions of a nonlinear second order m-point boundary value problem (m-PBVP) on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. AMS subject classification: 39A10, 34B18, 34B40, 45G10.