UNLABELLED:The prognostication of risk factors for the outcome of LCPD was examined. The radiographic results of conservative treatment with Thomas splint and operative treatment with intertrochanteric derotational varus osteotomy (DVO) were compared using the Index of Deformity (D).METHOD:Radiographs of 153 patients with unilateral LCPD were evaluated retrospectively 1.5-3 years and 3-7 years after diagnosis using the Index of Deformity and Index of Direction. We investigated the radiographic changes in relation to acetabular or metaphyseal reaction, Waldenström classification or limited range of motion at diagnosis and in dependence of therapy.RESULTS:There was a significant better acetabulum-head-index of deformity after DVO. Children with metaphyseal or acetabular reaction had bigger deformities. Patients with metaphyseal reaction had smaller deformities after DVO compared with conservative treatment. Free range of motion (ROM) was prerequisite for good results after DVO. Waldenström classification at diagnosis did not have any influence on morphologic changes after 3-7 years.CONCLUSION:DVO leads to a better containment than conservative treatment with Thomas splint, metaphyseal reaction should be an indication for operative treatment. Prerequisite for DVO is a free ROM. Because Waldenström class at diagnosis does not influence the outcome, free ROM before starting the treatment is more important than an immediate start of therapy.

Problem: The prognostication of risk factors for the outcome of LCPD was examined. The radiographic results of conservative treatment with Thomas splint and operative treatment with intertrochanteric derotational varus osteotomy (DVO) were compared using the Index of Deformity (D). Method: Radiographs of 153 patients with unilateral LCPD were evaluated retrospectively 1.5-3 years and 3-7 years after diagnosis using the Index of Deformity and Index of Direction. We investigated the radiographic changes in relation to acetabular or metaphyseal reaction, Waldenstrom classification or limited range of motion at diagnosis and in dependence of therapy. Results: There was a significant better acetabulum-head-index of deformity after DVO. Children with metaphyseal or acetabular reaction had bigger deformities. Patients with metaphyseal reaction had smaller deformities after DVO compared with conservative treatment. Free range of motion (ROM) was prerequisite for good results after DVO. Waldenstrom classification at diagnosis did not have any influence on morphologic changes after 3-7 years. Conclusion: DVO leads to a better containment than conservative treatment with Thomas splint, metaphyseal reaction should be an indication for operative treatment. Prerequisite for DVO is a free ROM. Because Waldenstrom class at diagnosis does not influence the outcome, free ROM before starting the treatment is more important than an immediate start of therapy.

Journal Article Rosenbrock Methods using few LU-Decompositions Get access PETER KAPS, PETER KAPS Institut für Mathematik und Geometrie, Universität InnsbruckTechnikerstraBe 13, A-6020 Innsbruck, Austria Search for other works by this author on: Oxford Academic Google Scholar ALEXANDER OSTERMANN ALEXANDER OSTERMANN Institut für Mathematik und Geometrie, Universität InnsbruckTechnikerstraBe 13, A-6020 Innsbruck, Austria Search for other works by this author on: Oxford Academic Google Scholar IMA Journal of Numerical Analysis, Volume 9, Issue 1, January 1989, Pages 15–27, https://doi.org/10.1093/imanum/9.1.15 Published: 01 January 1989 Article history Received: 11 May 1988 Published: 01 January 1989

Solving flame propagation problems with the method of lines leads to large systems of ordinary differential equations. These systems are usually solved by Backward Differentiation Formula (BDF) methods, such as by LSODE of Hindmarsh. Recently, Rosenbrock methods turned out to be rather successful for integrating small systems with inexpensive function and Jacobian evaluations. However, no test has been done on the performance of some recently developed Rosenbrock codes in a situation in which the dimension of the system is large, for example, over one hundred equations. These Rosenbrock codes performed quite well on the STIFF DETEST and other small systems. The aim of this paper is to investigate the performance of the Rosenbrock methods in solving the flame propagation problem by the method of lines.

In [16], Rosenbrock methods of order four are investigated using an embedded method of order three for step size control. Here, we study such a method using Richardson extrapolation for step size control and compare the two techniques with each other. The usual belief that extrapolation is inferior to embedding is not true. Numerical results for the 25 examples of STIFF DETEST and for some more difficult problems show the following behaviour: For low tolerances (∼10−2) embedding is superior, for moderate tolerances (∼10−4) both techniques are comparable and for high tolerances (<10−5) extrapolation is superior. Under certain conditions the extrapolated value can be used for step continuation without stability problems.

A semi-implicit Runge-Kutta method is proposed and application is made to models of chemical kinetics. The presented algorithm GRKV4 is based on an A-stable formula with variable order up to four and possesses an automatic stepsize control. The range of application of GRKV4 is discussed.

This paper deals with the solution of nonlinear stiff ordinary differential equations. The methods derived here are of Rosenbrock-type. This has the advantage that they areA-stable (or stiffly stable) and nevertheless do not require the solution of nonlinear systems of equations. We derive methods of orders 5 and 6 which require one evaluation of the Jacobian and oneLU decomposition per step. We have written programs for these methods which use Richardson extrapolation for the step size control and give numerical results.