@article{MTMT:34826715,
	title = {Method of fundamental solutions: New approximation results and applications},
	url = {https://m2.mtmt.hu/api/publication/34826715},
	author = {Hoang, Hieu T. and Izsák, Ferenc and Maros, Gábor},
	doi = {10.1016/j.cam.2024.115934},
	journal-iso = {J COMPUT APPL MATH},
	journal = {JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS},
	volume = {448},
	unique-id = {34826715},
	issn = {0377-0427},
	year = {2024},
	eissn = {1879-1778},
	orcid-numbers = {Izsák, Ferenc/0000-0001-7398-7318}
}

@article{MTMT:34751048,
	title = {Reduction of positive self-adjoint extensions},
	url = {https://m2.mtmt.hu/api/publication/34751048},
	author = {Tarcsay, Zsigmond and Sebestyén, Zoltán},
	doi = {10.7494/OpMath.2024.44.3.425},
	journal-iso = {OPUSC MATHEMATICA},
	journal = {OPUSCULA MATHEMATICA},
	volume = {44},
	unique-id = {34751048},
	issn = {1232-9274},
	year = {2024},
	pages = {425-438},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:34749280,
	title = {Reaction-diffusion equations on metric graphs with edge noise},
	url = {https://m2.mtmt.hu/api/publication/34749280},
	author = {Sikolya, Eszter},
	doi = {10.1007/s10476-024-00006-z},
	journal-iso = {ANAL MATH},
	journal = {ANALYSIS MATHEMATICA},
	unique-id = {34749280},
	issn = {0133-3852},
	abstract = {We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard continuity and generalized, non-local Neumann-Kirchhoff-type law in each vertex. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. The model is a generalization of the problem in [14] where polynomials with much more restrictive assumptions are considered and no first order differential operator is involved. We utilize the semigroup approach from [15] to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph.},
	year = {2024},
	eissn = {1588-273X},
	orcid-numbers = {Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:34435578,
	title = {A Functional Approach to Interpreting the Role of the Adjoint Equation in Machine Learning},
	url = {https://m2.mtmt.hu/api/publication/34435578},
	author = {Fekete, Imre and Molnár, András Sándor and Simon L., Péter},
	doi = {10.1007/s00025-023-02074-3},
	journal-iso = {RES MATHEM},
	journal = {RESULTS IN MATHEMATICS},
	volume = {79},
	unique-id = {34435578},
	issn = {1422-6383},
	abstract = {The connection between numerical methods for solving differential equations and machine learning has been revealed recently. Differential equations have been proposed as continuous analogues of deep neural networks, and then used in handling certain tasks, such as image recognition, where the training of a model includes learning the parameters of systems of ODEs from certain points along their trajectories. Treating this inverse problem of determining the parameters of a dynamical system that minimize the difference between data and trajectory by a gradient-based optimization method presents the solution of the adjoint equation as the continuous analogue of backpropagation that yields the appropriate gradients. The paper explores an abstract approach that can be used to construct a family of loss functions with the aim of fitting the solution of an initial value problem to a set of discrete or continuous measurements. It is shown, that an extension of the adjoint equation can be used to derive the gradient of the loss function as a continuous analogue of backpropagation in machine learning. Numerical evidence is presented that under reasonably controlled circumstances the gradients obtained this way can be used in a gradient descent to fit the solution of an initial value problem to a set of continuous noisy measurements, and a set of discrete noisy measurements that are recorded at uncertain times.},
	year = {2024},
	eissn = {1420-9012},
	orcid-numbers = {Fekete, Imre/0000-0001-8450-7631; Simon L., Péter/0000-0002-2183-1853}
}

@article{MTMT:34396234,
	title = {On the convergence of multiple Richardson extrapolation combined with explicit Runge–Kutta methods},
	url = {https://m2.mtmt.hu/api/publication/34396234},
	author = {Matebie, Teshome Bayleyegn and Faragó, István and Havasi, Ágnes},
	doi = {10.1007/s10998-023-00557-y},
	journal-iso = {PERIOD MATH HUNG},
	journal = {PERIODICA MATHEMATICA HUNGARICA},
	unique-id = {34396234},
	issn = {0031-5303},
	abstract = {The order of accuracy of any convergent time integration method for systems of differential equations can be increased by using the sequence acceleration method known as Richardson extrapolation, as well as its variants (classical Richardson extrapolation and multiple Richardson extrapolation). The original (classical) version of Richardson extrapolation consists in taking a linear combination of numerical solutions obtained by two different time-steps with time-step sizes h and h /2 by the same numerical method. Multiple Richardson extrapolation is a generalization of this procedure, where the extrapolation is applied to the combination of some underlying numerical method and the classical Richardson extrapolation. This procedure increases the accuracy order of the underlying method from p to p+2 p + 2 , and with each repetition, the order is further increased by one. In this paper we investigate the convergence of multiple Richardson extrapolation in the case where the underlying numerical method is an explicit Runge–Kutta method, and the computational efficiency is also checked.},
	year = {2024},
	eissn = {1588-2829},
	orcid-numbers = {Matebie, Teshome Bayleyegn/0000-0002-9277-4315; Faragó, István/0000-0002-4615-7615; Havasi, Ágnes/0000-0002-4125-4520}
}

@article{MTMT:34317106,
	title = {Operators on anti-dual pairs. Supremum and infimum of positive operators},
	url = {https://m2.mtmt.hu/api/publication/34317106},
	author = {Tarcsay, Zsigmond and Göde, Ábel},
	doi = {10.1016/j.jmaa.2023.127893},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {531},
	unique-id = {34317106},
	issn = {0022-247X},
	year = {2024},
	eissn = {1096-0813},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:34226995,
	title = {Quasi‐Newton variable preconditioning for nonlinear elasticity systems in 3D},
	url = {https://m2.mtmt.hu/api/publication/34226995},
	author = {Karátson, János and Sysala, S. and Béreš, M.},
	doi = {10.1002/nla.2537},
	journal-iso = {NUMER LINEAR ALGEBR},
	journal = {NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS},
	volume = {31},
	unique-id = {34226995},
	issn = {1070-5325},
	abstract = {Quasi‐Newton iterations are constructed for the finite element solution of small‐strain nonlinear elasticity systems in 3D. The linearizations are based on spectral equivalence and hence considered as variable preconditioners arising from proper simplifications in the differential operator. Convergence is proved, providing bounds uniformly w.r.t. the FEM discretization. Convenient iterative solvers for linearized systems are also proposed. Numerical experiments in 3D confirm that the suggested quasi‐Newton methods are competitive with Newton's method.},
	year = {2024},
	eissn = {1099-1506},
	orcid-numbers = {Karátson, János/0000-0003-1369-7743; Sysala, S./0000-0002-2704-4797; Béreš, M./0000-0001-8588-3268}
}

@article{MTMT:34209067,
	title = {Rates of robust superlinear convergence of preconditioned Krylov methods for elliptic FEM problems},
	url = {https://m2.mtmt.hu/api/publication/34209067},
	author = {Castillo, S. J. and Karátson, János},
	doi = {10.1007/s11075-023-01663-1},
	journal-iso = {NUMER ALGORITHMS},
	journal = {NUMERICAL ALGORITHMS},
	unique-id = {34209067},
	issn = {1017-1398},
	abstract = {This paper considers the iterative solution of finite element discretizations of second-order elliptic boundary value problems. Mesh independent estimations are given for the rate of superlinear convergence of preconditioned Krylov methods, involving the connection between the convergence rate and the Lebesgue exponent of the data. Numerical examples demonstrate the theoretical results.},
	year = {2024},
	eissn = {1572-9265},
	orcid-numbers = {Karátson, János/0000-0003-1369-7743}
}

@article{MTMT:34429674,
	title = {Symplectic time-domain finite element method (STD-FEM) extended with wave propagation in porous materials for automotive interior acoustic modeling},
	url = {https://m2.mtmt.hu/api/publication/34429674},
	author = {Huszty, Csaba György and Firtha, Gergely and Izsák, Ferenc},
	doi = {10.1088/1742-6596/2677/1/012010},
	journal-iso = {J PHYS CONF SER},
	journal = {JOURNAL OF PHYSICS-CONFERENCE SERIES},
	volume = {2677},
	unique-id = {34429674},
	issn = {1742-6588},
	abstract = {The prediction of sound field evolving inside automotive interiors has gained significant attention in recent years, both for acoustic design purposes and virtual reality applications. Recently, a novel numerical simulation method was proposed by the present authors termed as symplectic time-domain finite element method. This paper discusses the numerical method and its application for simulating sound fields inside vehicle interiors. The presented case study includes the effect of seat absorption and non-rigid boundaries by applying either locally reacting, or elastic surface models exhibiting extended reactivity. © Published under licence by IOP Publishing Ltd.},
	year = {2023},
	eissn = {1742-6596},
	orcid-numbers = {Izsák, Ferenc/0000-0001-7398-7318}
}

@article{MTMT:34121362,
	title = {Neural-Network-Assisted Finite Difference Discretization for Numerical Solution of Partial Differential Equations},
	url = {https://m2.mtmt.hu/api/publication/34121362},
	author = {Izsák, Ferenc and Izsák, Rudolf},
	doi = {10.3390/a16090410},
	journal-iso = {ALGORITHMS},
	journal = {ALGORITHMS},
	volume = {16},
	unique-id = {34121362},
	abstract = {A neural-network-assisted numerical method is proposed for the solution of Laplace and Poisson problems. Finite differences are applied to approximate the spatial Laplacian operator on nonuniform grids. For this, a neural network is trained to compute the corresponding coefficients for general quadrilateral meshes. Depending on the position of a given grid point x0 and its neighbors, we face with a nonlinear optimization problem to obtain the finite difference coefficients in x0. This computing step is executed with an artificial neural network. In this way, for any geometric setup of the neighboring grid points, we immediately obtain the corresponding coefficients. The construction of an appropriate training data set is also discussed, which is based on the solution of overdetermined linear systems. The method was experimentally validated on a number of numerical tests. As expected, it delivers a fast and reliable algorithm for solving Poisson problems.},
	year = {2023},
	eissn = {1999-4893},
	orcid-numbers = {Izsák, Ferenc/0000-0001-7398-7318}
}