Results 71 to 80 of about 2,048 (231)

Continuous analogue to iterative optimization for PDE-constrained inverse problems [PDF]

Inverse Problems in Science and Engineering, 2018
The parameters of many physical processes are unknown and have to be inferred from experimental data. The corresponding parameter estimation problem is often solved using iterative methods such as steepest descent methods combined with trust regions. For a few problem classes also continuous analogues of iterative methods are available.
Boiger, R., Fiedler, A., Hasenauer, J., Kaltenbacher, B.   +3 more
openaire   +3 more sources

New Drain Spacing Formulas Using the Variational Iteration Method

Irrigation and Drainage, EarlyView.
ABSTRACT In this study, the drain spacing is computed using the variational iteration method (VIM) to the linearized Boussinesq equation. By applying at most two iterations of the VIM method under three different initial condition scenarios, three equations for drain spacing calculation were derived. These equations predict values of drain spacing that
George Kargas, Leonidas Mindrinos, Paraskevi Londra   +2 more
wiley   +1 more source

Application of the inverse Laplace transform techniques to solve the generalized Bagley–Torvik equation including Caputo’s fractional derivative

Partial Differential Equations in Applied Mathematics
This article employs the Laplace transform approach to solve the Bagley–Torvik equation including Caputo’s fractional derivative. Laplace transform is a powerful method for enabling solving integer and non-integer order ODEs and PDEs in engineering and ...
Dania Santina, Kamran, Muhammad Asif, Salma Aljawi, Nabil Mlaiki   +4 more
doaj   +1 more source

Uniqueness for Neumann Problems for Nonlinear Elliptic Equations With Lower Order Terms

Mathematische Nachrichten, EarlyView.
ABSTRACT In this paper, we prove uniqueness results for weak solutions to a class of Neumann problems, whose prototype is λ(1+u2)(p−2)/2u−div((1+|∇u|2)(p−2)/2∇u)−div(c(x)(1+|u|2)(τ+1)/2)+b(x)(1+|∇u|2)(σ+1)/2=finΩ(1+|∇u|2)(p−2)/2∇u+c(x)(1+|u|2)(τ+1)/2)·n̲=0on∂Ω,$$\begin{equation*} {\begin{cases} {}\lambda {(1+ u^2)}^{(p-2)/2}u-{\operatorname{div}}({(1+|\
Maria Francesca Betta, Olivier Guibé, Anna Mercaldo, Maria Rosaria Posteraro   +3 more
wiley   +1 more source

Numerical differentiation of fractional order derivatives based on inverse source problems of hyperbolic equations

Mathematical Modelling and Analysis
In this paper, we mainly study the numerical differentiation problem of computing the fractional order derivatives from noise data of a single variable function.
Zewen Wang, Shufang Qiu, Xiuxing Rui, Wen Zhang   +3 more
doaj   +1 more source

Meshless solutions of PDE inverse problems on irregular geometries

CoRR
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral bases on arbitrary spatiotemporal domains, whereby the basis is defined on a hyperrectangle containing the true ...
James V. Roggeveen, Michael P. Brenner
openaire   +2 more sources

Unveiling New Perspectives on the Hirota–Maccari System With Multiplicative White Noise

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this study, we delve into the stochastic Hirota–Maccari system, which is subjected to multiplicative noise according to the Itô sense. The stochastic Hirota–Maccari system is significant for its ability to accurately model how stochastic affects nonlinear wave propagation, providing valuable insights into complex systems like fluid dynamics
Mohamed E. M. Alngar, Khaled A. Gepreel, Reham M. A. Shohib, Yakup Yildirim   +3 more
wiley   +1 more source

An Adaptive Sampling Algorithm with Dynamic Iterative Probability Adjustment Incorporating Positional Information

Entropy
Physics-informed neural networks (PINNs) have garnered widespread use for solving a variety of complex partial differential equations (PDEs). Nevertheless, when addressing certain specific problem types, traditional sampling algorithms still reveal ...
Yanbing Liu, Liping Chen, Yu Chen, Jianwan Ding   +3 more
doaj   +1 more source

Exact Solutions of Linear Multiple Delay Partial Differential Equations

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This paper develops an analytical framework for linear differential equations with multiple discrete delays. A new function, referred to as the multiple‐delay exponential function, is introduced, and some of its fundamental properties are established.
Stuart‐James M. Burney
wiley   +1 more source

Direct and inverse source problems for degenerate parabolic equations [PDF]

, 2020
Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied ...
Kostin, AB, Kamynin, VL, Hussein, MS, Lesnic, D   +3 more
core   +1 more source