Results 31 to 40 of about 83,156,277 (277)

Semi-Implicit Multistep Extrapolation ODE Solvers

Mathematics, 2020
Multistep methods for the numerical solution of ordinary differential equations are an important class of applied mathematical techniques. This paper is motivated by recently reported advances in semi-implicit numerical integration methods, multistep and
Denis Butusov, Aleksandra Tutueva, Petr Fedoseev, Artem Terentev, Artur Karimov   +4 more
doaj   +1 more source

Continuous Runge–Kutta schemes for pantograph type delay differential equations

Partial Differential Equations in Applied Mathematics
Pantograph differential equations are important types of delay differential equations. Using continuous mono-implicit RK schemes, we propose a numerical method for numerically approximating pantograph delay differential equations that are reliable and ...
Fathalla A. Rihan
doaj   +1 more source

Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

Mathematics, 2021
In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation.
Janez Urevc, Miroslav Halilovič
doaj   +1 more source

Super class of implicit extended backward differentiation formulae for the numerical integration of stiff initial value problems [PDF]

Computational Algorithms and Numerical Dimensions
An implicit Superclass of non-block Extended Backward Differentiation Formulae (SEBDF) for the numerical integration of first-order stiff system of Ordinary Differential Equations (ODEs) in Initial Value Problems (IVPs) with optimal stability properties ...
Hamisu Musa, Buhari Alhassan
doaj   +1 more source

Direct numerical simulation of turbulence at lower costs [PDF]

, 1995
Direct Numerical Simulation (DNS) is the most accurate, but also the most expensive, way of computing turbulent flow. To cut the costs of DNS we consider a family of second-order, explicit one-leg time-integration methods and look for the method with the
Veldman, A.E.P., Verstappen, R.W.C.P., Verstappen, R.W.C.P.,, Veldman, A.E.P.,, R.W.C.P. Verstappen, A.E.P. Veldman   +5 more
core   +3 more sources

High order boundary value linear multistep method for the numerical solution of IVPs in ODEs

Journal of Nigerian Society of Physical Sciences
In this paper, we introduce High order boundary value linear multistep method (HOBVLMM) for the numerical solution of stiff systems of initial value problems (IVPs).
Seun Ogunfeyitimi, Monday Ikhile, Peter Olatunji   +2 more
doaj   +1 more source

Advances in Parameter Estimation and Learning from Data for Mathematical Models of Hepatitis C Viral Kinetics

Mathematics, 2022
Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy.
Vladimir Reinharz, Alexander Churkin, Harel Dahari, Danny Barash   +3 more
doaj   +1 more source

Numerical methods for extremely stiff systems of ordinary differential equations

Applied Mathematical Modelling, 1979
Computer simulation of dynamic systems very often leads to the solution of a set of stiff ordinary differential equations. The solution of this set of equations involves the eigenvalues of its Jacobian matrix. The greater the spread in eigenvalues, the more time consuming the solutions become when existing numerical methods are employed.
Bui, T. D., Bui, T. R.
openaire   +1 more source

High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling [PDF]

, 2014
Copyright @ 2014 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.We revisit a method ...
Mark P Brewin, Shuhua Hu, Simon Shaw, Carola Kruse, Birch, MJ, Zackary R Kenz, Kruse, C, Brewin, MP, John R Whiteman, Maischak, M, Banks, HT, Malcolm J Birch, H. T. Banks, Stephen E Greenwald, Greenwald, SE, Kenz, ZR, Matthias Maischak, Whiteman, JR, Hu, S, Shaw, S   +19 more
core   +1 more source

Towards Numerical Method-Informed Neural Networks for PDE Learning

Mathematics
Solving stiff partial differential equations with neural networks remains challenging due to the presence of multiple time scales and numerical instabilities that arise during training. This paper addresses these limitations by embedding the mathematical
Pasquale De Luca, Livia Marcellino
doaj   +1 more source