26 citations · 42 across the 8 of their papers we have counts for
8 papers
Neural Network-Assisted Refinement of Traditional Schemes for One-Dimensional Scalar Conservation Laws
Imre Fekete, Ferenc Izsák, Vendel P. Kupás
A clear link is established between conventional numerical methods and neural network approximations for solving one-dimensional scalar conservation laws. The focus is on the const…
Tolerance Proportionality and Computational Stability in Adaptive Parallel-in-Time Runge-Kutta Methods
Imre Fekete, Ferenc Izsák, Vendel P. Kupás +1
In this paper, we investigate how adaptive time-integration strategies can be effectively combined with parallel-in-time numerical methods for solving systems of ordinary different…
Linear multistep methods with repeated global Richardson extrapolation
Imre Fekete, Lajos Lóczi
In this work, we further investigate the application of the well-known Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear mult…
Linear multistep methods and global Richardson extrapolation
Imre Fekete, Lajos Lóczi
In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMM…
Learning the parameters of a differential equation from its trajectory via the adjoint equation
Imre Fekete, András Molnár, Péter L. Simon
The paper contributes to strengthening the relation between machine learning and the theory of differential equations. In this context, the inverse problem of fitting the parameter…
Embedded error estimation and adaptive step-size control for optimal explicit strong stability preserving Runge--Kutta methods
Sidafa Conde, Imre Fekete, John N. Shadid
We construct a family of embedded pairs for optimal strong stability preserving explicit Runge-Kutta methods of order to be used to obtain numerical solution of s…
On the zero-stability of multistep methods on smooth nonuniform grids
Gustaf Söderlind, Imre Fekete, István Faragó
In order to be convergent, linear multistep methods must be zero stable. While constant step size theory was established in the 1950's, zero stability on nonuniform grids is less w…
Positivity for convective semi-discretizations
Imre Fekete, David I. Ketcheson, Lajos Lóczi
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to…