Essays about: "variable step-size"

Showing result 1 - 5 of 9 essays containing the words variable step-size.

  1. 1. Comparing Multistep Methods Within Parametric Classes to Determine Viability in Solver Applications

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Michael Andrew Kraut; [2021]
    Keywords : Ordinary Differential Equations; Initial Value Problems; Linear Multistep Methods; Numerical Analysis; Numerical Solvers; Parametrized; Algorithms; Control Theory; Mathematics and Statistics;

    Abstract : In the 2017 paper by Arévalo and Söderlind, a framework was established for creating linear multistep methods of various classes based on a polynomial formulation which includes variable step size adaptivity. These classes are: k step explicit and implicit methods of order k and k+1 respectively for nonstiff problems (such as Adams methods), and k step implicit methods of order k for stiff problems (such as BDF methods). READ MORE

  2. 2. Construction and benchmarking of adaptive parameterized linear multistep methods

    University essay from Lunds universitet/Matematik LTH

    Author : Josefine Olander; Erik Jonsson Glans; [2016]
    Keywords : Linear multistep method; matlab software; variable step-size; variable order; numerical solver of ODEs; Mathematics and Statistics; Technology and Engineering;

    Abstract : A recent publication introduced a new way to define all k-step linear multistep methods of order k and k+1, in a parametric form that builds in variable step-size. In this framework it is possible to continuously change method and step-size, making it possible to create better behaving adaptive numerical solvers. READ MORE

  3. 3. Common Envelope Evolution

    University essay from Lunds universitet/Astronomi

    Author : Robert Wissing; [2016]
    Keywords : Physics and Astronomy;

    Abstract : We present simulations done on the onset of common envelope evolution with giant donors by taking into account the mass loss through the outer Lagrange point and the forming of the common envelope. In addition we apply proper stellar models and evolve our simulations using an Runge-Kutta integrator with adaptive step-size. READ MORE

  4. 4. Analysis and Implementation of Adaptive Explicit Two-Step Methods

    University essay from Lunds universitet/Matematik LTH

    Author : Kjartan Kari Gardarsson Myrdal; [2015]
    Keywords : numerical methods; two-step; variable; multistep methods; ODE; adaptive; differential equations; parametric; explicit; Mathematics and Statistics;

    Abstract : Recently a new way of constructing variable step-size multistep methods has been proposed, that parametrizes the entire domain of multistep methods. In the presented work the case of explicit two-step methods is looked at, analyzed and related to the already known theory of multistep methods. READ MORE

  5. 5. A Python Implementation of Explicit 2-step Methods

    University essay from Lunds universitet/Matematik LTH

    Author : Kevin Persson; [2015]
    Keywords : Mathematics and Statistics;

    Abstract : This paper shows the Python implementation of a new way of constructing a variable multistep ODE solver which is not based on extending fixed step-size methods but rather on defining interpolation and collocation conditions for each new point. The implementation allows for any explicit 2-step method of order 2... READ MORE