Neumaier’s Method For The Solution Of Initial Value Problems For Stiff Ordinary Differential Equations [PDF]
, 2005 Compared with standard numerical methods for initial value problems (IVPs) for ordinary differential equations (ODEs), validated methods not only compute a numerical solution to a problem, but also generate a guaranteed bound on the global error ...
Annie Hsiao Chen Yuk
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Defect correction techniques for stiff initial value problems [PDF]
, 2003 In the talk given by W.Auzinger it is shown that certain modified defect correction algorithms based on techniques like defect interpolation (IPDeC) and defect quadrature (IQDeC) enable the efficient iterative realization of superconvergent collocation ...
Hofstätter, Harald +3 more
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The Finite Element Method for Stiff Ordinary Differential Equations
AppliedMathThe paper utilizes the continuous finite element method to solve stiff ordinary differential equations and proves that the linear finite element method and the quadratic finite element method have A-stability in solving autonomous ordinary differential ...
Yanhui Ding, Qiong Tang, Sijia Tang
doaj +1 more source
Tendler-like Formulas for Stiff ODEs
Abstract This paper proves a convergence result for a general class of methods for the solution of ordinary differential equations (initial value problems). The proof uses standard results from the theory of matrix polynomials. We present new cyclic linear multistep formulas of orders 3 to 9 for stiff equations, which, order by order ...
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On transformations of graded matrices, with applications to stiff ODE's
Numerische Mathematik, 1985 The author presents an iterative block LR refining algorithm for graded matrices together with its application to the approximate solution of singularly perturbed systems of ordinary differential equations with several parameters. A block matrix \(A=[A_{ij}]\), \(i,j=1,2,...,m\), where \(A_{ij}\) are \((n_ i\times n_ j)\) matrices, is called a graded ...
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SPIN-ODE: Stiff Physics-Informed Neural ODE for Chemical Reaction Rate Estimation
Estimating rate coefficients from complex chemical reactions is essential for advancing detailed chemistry. However, the stiffness inherent in real-world atmospheric chemistry systems poses severe challenges, leading to training instability and poor convergence, which hinder effective rate coefficient estimation using learning-based approaches.
Boy Michael +3 more
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Block backward differentiation alpha-formulas for solving stiff ordinary differential equations [PDF]
, 2017 A new family of block methods, namely block backward differentiation alpha-formulas (BBDF-) are developed for solving first and second order stiff ordinary differential equations (ODEs) directly.
Mohd Zawawi, Iskandar Shah
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Weighted block Runge-Kutta method for solving stiff ordinary differential equations [PDF]
, 2016 In this paper, weighted block Runge-Kutta (WBRK) method is derived for solving stiff ordinary differential equations (ODEs). Implementation of weights on the method and its stability region are shown.
Jana Aksah, Saufianim +4 more
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PEtab.jl: advancing the efficiency and utility of dynamic modelling. [PDF]
BioinformaticsPersson S +7 more
europepmc +2 more sources
HySimODE: a hybrid stochastic-deterministic simulation framework for multiscale models of biological systems. [PDF]
BioinformaticsZamora-Chimal CG, Darlington APS.
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