Results 41 to 50 of about 843 (137)

A Picard-Lindelöf theorem for smooth PDE [PDF]

, 2022
Paolo Robuffo Giordano, Lorenzo Luperi Baglini   +1 more
openalex   +1 more source

Global Flows with Invariant Measures for the Inviscid Modified SQG Equations

, 2017
We consider the family known as modified or generalized surface quasi-geostrophic equations (mSQG) consisting of the classical inviscid surface quasi-geostrophic (SQG) equation together with a family of regularized active scalars given by introducing a ...
Nahmod, Andrea, Pavlovic, Natasa, Staffilani, Gigliola, Totz, Nathan   +3 more
core   +1 more source

Challenges in Automatic Differentiation and Numerical Integration in Physics‐Informed Neural Networks Modelling

International Journal for Numerical Methods in Engineering, Volume 126, Issue 20, 30 October 2025.
ABSTRACT In this paper, we numerically examine the precision challenges that emerge in automatic differentiation and numerical integration in various tasks now tackled by physics‐informed neural networks (PINNs). Specifically, we illustrate how ill‐posed problems or inaccurately computed functions can cause serious precision issues in differentiation ...
Josef Daněk, Jan Pospíšil
wiley   +1 more source

Dynamical analysis of tumor–dystrophin interaction model with impact of age of onset and staging

Fixed Point Theory and Algorithms for Sciences and Engineering
In this research work, the authors present a mathematical model to study the biological interplay between tumor growth, dystrophin protein, and the impact of age of onset and staging through a system of ordinary differential equations (ODEs).
Ausif Padder, Sania Qureshi, R. S. Dubey, Mehraj ud Din Rather, Afroz Afroz   +4 more
doaj   +1 more source

Solutions to ordinary differential equations at infinity [PDF]

, 2022
I denne teksten skal vi se på løsninger til førsteordens ordinære differensiallikninger når t går mot uendelig. Vi vil ts for oss tre tilfeller av ordniære differensiallikninger og se på hva slags kriterier vi trenger for at en løsning skal eksistere ...
Kristengård, Silje Heggen
core  

Augury and Forerunner: Real‐Time Feedback Via Predictive Numerical Optimization and Input Prediction

Computer Graphics Forum, Volume 44, Issue 6, September 2025.
Transient information generated by solver steps can inform future objective function minimization. In Augury, we explore the impact of predictive numerical optimization by using solver history to predict future minimization solutions, reducing computational resources needed to arrive at convergent states for a broad class of gradient‐based optimization
J. Graus, Y. Gingold
wiley   +1 more source

Qualitative analysis of dynamic equations on time scales

Electronic Journal of Differential Equations, 2018
In this article, we establish the Picard-Lindelof theorem and approximating results for dynamic equations on time scale. We present a simple proof for the existence and uniqueness of the solution.
Syed Abbas
doaj  

A Discontinuous Galerkin Method for Simulating 3D Seismic Wave Propagation in Nonlinear Rock Models: Verification and Application to the Mw 7.8 2015 Gorkha, Nepal Earthquake

Journal of Geophysical Research: Solid Earth, Volume 130, Issue 7, July 2025.
Abstract The nonlinear mechanical responses of rocks and soils to seismic waves play an important role in earthquake physics, influencing ground motion from source to site. Continuous geophysical monitoring, such as ambient noise interferometry, has revealed co‐seismic wave speed reductions extending tens of kilometers from earthquake sources. However,
Zihua Niu, Alice‐Agnes Gabriel, Sebastian Wolf, Thomas Ulrich, Vladimir Lyakhovsky, Heiner Igel   +5 more
wiley   +1 more source

Analysis of a Radiotherapy Model for Brain Tumors

Studies in Applied Mathematics, Volume 155, Issue 1, July 2025.
ABSTRACT In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors undergoing radiotherapy treatment. Under certain assumptions regarding the given data in the model, we prove the existence and uniqueness of a weak nonnegative (biologically relevant) solution.
Marina Chugunova, Hangjie Ji, Roman Taranets, Nataliya Vasylyeva   +3 more
wiley   +1 more source

Forward‐looking experimentation of correlated alternatives

Theoretical Economics, Volume 20, Issue 3, Page 883-909, July 2025.
This paper studies how a forward‐looking decision maker experiments on unknown alternatives of correlated utilities. The utilities are modeled by a Brownian motion such that similar alternatives yield similar utilities. Experimentation trades off between the continuation value of exploration and the opportunity cost of exploitation.
Yu Fu Wong
wiley   +1 more source