20 papers · ranked by Valyu relevance
Kiyuob Jung
This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat's theorem and quasi-Mean Value Theorem. As an application, this paper develops several numerical schemes for solving initial value problems for first-order ordinary…
Alexander Rothkopf, W. A. Horowitz, Jan Nordström
In this contribution we present recent developments in the formulation and solution of Initial Boundary Value Problems (IBVPs). Building upon a modern variational action formulation of classical dynamics, we treat Initial Boundary Value Problems directly on the action level, bypassing governing equations. We show that…
Shadimetov, Kh. M., R.S. Karimov
This work presents problems of constructing finite-difference formulas in the Hilbert space, i.e., setting problems of constructing finite-difference formulas using functional methods. The work presents a functional statement of the problem of optimizing finite-difference formulas in the space W (m,m−1) 2 (0, 1). Here…
Xianke Wang, Shichao Yi, Huangliang Gu, Jing Xu + 1 more
This study tackles the numerical challenges posed by solutions with steep gradients in the Burgers equation, particularly poor stability in high-gradient regions and the ill-posedness of inverse problems in shock wave modeling. We propose a Weak-Form Physics-Informed Neural Network (WF-PINN) that fundamentally enhances…
Aamna Amer, Emad K. Jaradat, Hamood Ur Rehman, Yakup Yildirim + 2 more
This article introduces new optical soliton solutions for a fractional version of the quadratic-cubic nonlinear Schrödinger equation that describes the transmission of optical pulses in fiber optic systems with superfast fibers. The solutions are obtained using the modified Sardar sub-equation method and the…
Konstantinos Kalimeris, Leonidas Mindrinos
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In this work we focus on the heat equation on a finite interval and we determine the dimensionless diffusion parameter from a single measurement.…
Iryna Karpenko
In this work, we study the initial-boundary value (IBV) problems for the sine-Gordon (sG) equation in the light-cone coordinates $u_{xt}=\sin u$ in the quarter-planes x> 0, t > 0 x > 0 , t > 0 and x 0 x 0, assuming a suitable decay as $x\rightarrow +\infty$ or as $x\rightarrow -\infty$. Employing the Riemann-Hilbert…
Élise Foulatier, Pierre-Alain Boucard, François Louf, David Néron + 1 more
Simulating flow problems is at the core of many engineering applications but often requires high computational effort, especially when dealing with complex models. This work presents a novel approach for resolving flow problems using the LATIN-PGD solver. In this contribution, we place ourselves within the framework of…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Rudra Prakash, Shaunak Sen
The paper addresses the critical challenge of accurately characterising steady states in biomolecular systems, which are often complex, nonlinear, multistable and subject to significant uncertainties. Traditional numerical methods often fail to provide complete or guaranteed solutions under these conditions. To…
Andreas Chatziafratis, Sergey A. Rukolaine, Elias C. Aifantis
We obtain novel integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous initial-boundary-value as well as interface problems for the Barenblatt-Zheltov-Kochina pseudo-parabolic equation of Sobolev-Galpern type formulated on the real line, half-line…
V.V. Kryzhniy
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for resolving ill-posed problems. Central to our approach is high-degree…
Wenrui Hao, Lili Ju, Yuejin Xu
In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann boundary condition posed on general irregular domains. The DDM employs a phase-field function to extend the original parabolic problem to a…
Josefa Caballero, Łukasz Płociniczak, Kishin Sadarangani
We study a class of nonlinear Volterra integral equations that generalize the classical capillary rise models, allowing for nonsmooth kernels and nonlinearities. To accommodate such generalities, we work in two families of function spaces: spaces with prescribed modulus of continuity and integral H¨older spaces. We…
Niklas Neubrand, Timo Rachel, Tim Litwin, Jens Timmer + 2 more
Systems biology strives to unravel the complex dynamics of cellular processes, often with the help of ordinary differential equations (ODEs). However, the sparsity of measured data and the strong non-linearity of common ODEs introduce severe numerical problems in typical modeling tasks. This gave rise to the…
Authors not listed
Two kinetic schemes of the general modifier mechanism have been analysed in a quasi-steady state approximation, assuming that the reaction product concentration is negligible (a natural assumption for the initial rate method) and without additional simplifying assumptions. The characteristic equations have been…
Stephan Grein, David R. Penas, Daniel Weindl, Polina Lakrisenko + 2 more
Dynamic models are central to the computational life sciences but typically contain unknown parameters that must be inferred from experimental data. High-throughput measurements have made this task increasingly challenging, yielding high-dimensional search spaces and non-convex objectives with many local optima. This…
Dongmei Zhu, Ashley Davey, Harry Zheng
We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual value function and find a critical wealth level that determines if the…
Authors not listed
The political, social and economic consequences of climate change drastically influence the requirements of modern energy systems and its components. This includes not only energy production but also concepts and innovations for its storage, especially in magnitudes of gigawatt hours. Carnot batteries, which convert…
Andrea Polo-Rodríguez, David R. Penas, Julio R. Banga
Parameter estimation is a central challenge in systems biology, particularly for large dynamic models described by nonlinear ordinary differential equations (ODEs). These global optimization problems exhibit landscapes which are topologically heterogeneous, often exhibiting a pathological mixture of stiff, smooth…