The time evolution of spectral discretizations of hyperbolic systems

A Chebyshev collocation spectral method, applied to hyperbolic systems is considered, particularly for those initial boundary value problems which possess only solutions tending to zero at large times. It is shown that the numerical solutions of the system will also vanish at infinity, if and only if, the numerical solution of a scalar equation of the same type does. This result is then generalized for other spectral approximations

A review of spectral methods

An outline for spectral methods for partial differential equations is presented. The basic spectral algorithm is defined, collocation are emphasized and the main advantage of the method, the infinite order of accuracy in problems with smooth solutions are discussed. Examples of theoretical numerical analysis of spectral calculations are presented. An application of spectral methods to transonic flow is presented. The full potential transonic equation is among the best understood among nonlinear equations

Stability analysis of spectral methods for hyperbolic initial-boundary value systems

A constant coefficient hyperbolic system in one space variable, with zero initial data is discussed. Dissipative boundary conditions are imposed at the two points x = + or - 1. This problem is discretized by a spectral approximation in space. Sufficient conditions under which the spectral numerical solution is stable are demonstrated - moreover, these conditions have to be checked only for scalar equations. The stability theorems take the form of explicit bounds for the norm of the solution in terms of the boundary data. The dependence of these bounds on N, the number of points in the domain (or equivalently the degree of the polynomials involved), is investigated for a class of standard spectral methods, including Chebyshev and Legendre collocations

Convergence of spectral methods for hyperbolic initial-boundary value systems

A convergence proof for spectral approximations is presented for hyperbolic systems with initial and boundary conditions. The Chebyshev collocation is treated in detail, but the final result is readily applicable to other spectral methods, such as Legendre collocation or tau-methods

Non-reflecting boundary conditions for the compressible Navier-Stokes equations

A small perturbation analysis, in the long wavelength regime, is used to obtain the downstream boundary condition for the pressure for the flow over a flat plate. The methodology is extendable to other geometries. Numerical results for high Reynolds number laminar flows show great improvement in convergence rate to steady state as well as the quality of the results

Spectral methods for exterior elliptic problems

Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases

Depression and Diabetes Treatment Nonadherence: A Meta-Analysis

OBJECTIVE—Depression is common in patients with diabetes and is associated with worse treatment outcomes. Its relationship to treatment adherence, however, has not been systematically reviewed. We used meta-analysis to examine the relationship between depression and treatment nonadherence in patients with type 1 and type 2 diabetes

Depression and Diabetes Treatment Nonadherence: A Meta-Analysis

OBJECTIVE—Depression is common in patients with diabetes and is associated with worse treatment outcomes. Its relationship to treatment adherence, however, has not been systematically reviewed. We used meta-analysis to examine the relationship between depression and treatment nonadherence in patients with type 1 and type 2 diabetes

Racial Disparities in the Treatment of Depression in Low-Income Persons With Diabetes

Individuals with diabetes are at higher risk for depression than the general population. Although depression can be treated with antidepressant medications, patients with diabetes and comorbid depression often go untreated. The goal of this study was to examine racial disparities in the treatment of depression with antidepressant medication in the southeastern U.S

Does treatment of subsyndromal depression improve depression and diabetes related outcomes: protocol for a randomised controlled comparison of psycho-education, physical exercise and treatment as usual

<p>Abstract</p> <p>Background</p> <p>The prevalence of mood difficulties in persons with diabetes is approximately twice that in the general population, affecting the health outcomes and patients' quality of life in an undesirable way. Although subsyndromal depression is an important predictor of a more serious clinical depression, it is often overlooked. This study aims to compare the effects of two non-pharmacological interventions for subsyndromal depression, psychoeducation and physical exercise, with diabetes treatment as usual on mood- and diabetes-related outcomes.</p> <p>Methods and Design</p> <p>Type 2 diabetic patients aged 18-65 yrs. who report mood difficulties and the related need for help in a mail survey will be potential participants. After giving informed consent, they will be randomly assigned to one of the three groups (psychoeducation, physical activity, treatment as usual). Depressive symptoms, diabetes distress, health-related quality of life and diabetes self-care activities will be assessed at baseline, at 6 weeks, 6 months and 12 months. A structured clinical interview for DSM-IV Axis I Disorders (SCID-I) will be performed at baseline and at one-year follow-up in order to determine the clinical significance of the patients' depressive symptoms. Disease-related data will be collected from patients' files and from additional physical examinations and laboratory tests.</p> <p>The two interventions will be comparable in terms of format (small group work), duration (six sessions) and approach (interactive learning; supporting the participants' active roles). The group treated as usual will be informed about their screening results and about the importance of treating depression. They will be provided with brief re-education on diabetes and written self-help instructions to cope with mood difficulties.</p> <p>Primary outcomes will be depressive symptoms. Secondary outcomes will be glycaemic control, diabetes-related distress, self-management of diabetes and health-related quality of life. Tertiary outcomes will be biochemical markers reflecting common pathophysiological processes of insulin resistance, inflammation and oxidative damage that are assumed to be intertwined in both diabetes and depression. The mixed-effect linear model will be used to compare the outcome variables.</p> <p>Power analysis has indicated that the two intervention groups and the control group should comprise 59 patients to enable detection of clinically meaningful differences in depressive symptoms with a power of 80% and alpha = 0.05. Outcomes will be analysed on an intention-to-treat basis.</p> <p>Trial Registration</p> <p>ISRCTN: <a href="http://www.controlled-trials.com/ISRCTN05673017">ISRCTN05673017</a></p