Date of Online Publication: 31/03/2006 Keywords: Ordinary differential equations, boundary value problems, collocation, residual, Authors: J. Kierzenka, L.F. Shampine Pages: 27-41 We describe the algorithms and implementation of the bvp5c program for solving boundary value problems (BVPs) for ordinary differential equations. A remarkable relationship between scaled residual and true error is established for the four-point […]
Keywords: circular cylinder, wall-mounted, LES, DES, imaging measurements Abstract: Numerical simulations of the turbulent separated flow around a wall-mounted finite cylinder were performed in order to assess the predictive accuracy of the methods for the unsteady flow field at high Reynolds number. While the results obtained from Large-Eddy Simulation show only minor diferences to experiments,
Date of Online Publication: 31/03/2008 Keywords: Ordinary differential equations; initial value problems; numerical differential, equations; numerical integration; extrapolation methods; rounding error accumulation; NDSolve Authors: Mark Sofroniou, Giulia Spaletta Pages: 105-121 This article outlines design and implementation details of the framework for one step methods for solving ordinary differential equations in Mathematica. The solver breaks up
Keywords: Backward Difference Formula; Circuit simulation; Differential-algebraic equations; Discretization error; Multirate; Numerical time integration; Partitioning; Transient analysis Abstract: Transient analysis is an important circuit simulation technique. The circuit model, which is a system of differential-algebraic equations, is solved for a given initial condition using numerical time integration techniques. Multirate methods are efficient if the dynamical
Date of Online Publication: 31/03/2008 Keywords: MOL, Method of Lines Authors: R. Knapp Pages: 43-59 Mathematica’s NDSolve command includes a general solver for partial differential equations based on the method of lines. Starting from a symbolic expression for the PDE a symbolic general representation of the spatial discretization is constructed which is finalized once the
Date of Online Publication: 31/03/2008 Keywords: Initial-value problem, ordinary differential equation, event location, root-finding, generalized eigenvalues, companion matrix pencil, Hermite interpolation problem,B�zout matrix Authors: Robert M. Corless, Azar Shakoori, D.A. Aruliah, Laureano Gonzalez-Vega Pages: 1-16 Continuous extensions are now routinely provided by many IVP solvers, for graphical output, error control, or event location. Recent developments
Keywords: predator-prey model, equilibria, stochastic diferential equation, stochastic stability. Abstract: We develop a mathematical model for understanding the e ect of wanderer spiders as biological controllers of the insects infesting vineyards, thus accounting also for the role played by residual wood and green patches as spiders habitat in the otherwise homogeneuous landscape of the Langhe
Keywords: fundamental solution method, periodic plane elasticity Abstract: We present a fundamental solution method for elasticity problems of planes with one-dimensional periodic structure, to which it is difficult to apply the conventional fundamental solution method. We propose an approximate solution of the fundamental solution method which is modi ed so that it is suitable to
Date of Online Publication: 31/03/2008 Keywords: Delay differential equations (DDEs); Event location; Ordinary differential, equations (ODEs); Problem solving environment (PSE); State-dependent impulses; Timedependent impulses Authors: S.P. Corwin, S. Thompson, S.M. White Pages: 139-149 This paper deals with the solution of systems of ordinary differential equations (ODEs) and systems of delay differential equations (DDEs) in which
Date of Online Publication: 31/03/2008 Keywords: Software, ODE solvers, code generation, bifurcation, continuation, delay – differential equation Authors: Warren Weckesser Pages: 151-165 Download PDF