The cost as a function of the number of experiments for a non‐symmetric 21×21$$ 21\times 21 $$ system. Four approaches are shown: the proposed stochastic conjugate gradient ILC (SCGILC) method (), deterministic conjugate gradient ILC (), stochastic gradient descent ILC () and deterministic gradient descent ILC ().
Leontine Aarnoudse, Tom Oomen
wiley +1 more source
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the ...
Winicour Jeffrey
doaj
On the initial value problem for the wave equation in Friedmann-Robertson-Walker space-times. [PDF]
Abbasi B, Craig W.
europepmc +1 more source
Stiffness in numerical initial-value problems
AbstractThis paper reviews various aspects of stiffness in the numerical solution of initial-value problems for systems of ordinary differential equations.In the literature on numerical methods for solving initial value problems the term “stiff” has been used by various authors with quite different meanings, which often causes confusion.
openaire +2 more sources
Performance Triggered Adaptive Model Reduction for Soil Moisture Estimation in Precision Irrigation
ABSTRACT Accurate soil moisture information is essential for precise irrigation to enhance water use efficiency. Estimating soil moisture based on limited soil moisture sensors is especially critical for obtaining comprehensive soil moisture information when dealing with large‐scale agricultural fields.
Sarupa Debnath+4 more
wiley +1 more source
The Initial-Value Problem for a Slab. II. Nonuniform Slab [PDF]
Janusz Mika
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Current and Future Cornea Chip Models for Advancing Ophthalmic Research and Therapeutics
This review analyzes cornea chip technology as an innovative solution to corneal blindness and tissue scarcity. The examination encompasses recent developments in biomaterial design and fabrication methods replicating corneal architecture, highlighting applications in drug screening and disease modeling while addressing key challenges in mimicking ...
Minju Kim+3 more
wiley +1 more source
Fractional differential equation with the fuzzy initial condition
In this paper we study the existence and uniqueness of the solution for a class of fractional differential equation with fuzzy initial value. The fractional derivatives are considered in the Riemann-Liouville sense.
Sadia Arshad, Vasile Lupulescu
doaj
Nonlinear hyperbolic initial value problem
AbstractThe nonlinear hyperbolic equation ∂2u(x, y)∂x ∂y + g(x, y)f(u(x, y)) = 0 with u(x, 0) = φ(x) and u(0, y) = Ψ(y), considered by Hsiang and Kwong (J. Math. Anal. Appl., 85 (1982), 31–45) under appropriate smoothness conditions, is solvable by the author's decomposition method (“Stochastic Systems,” Academic Press, 1983 and “Nonlinear Stochastic ...
openaire +2 more sources
Well-posedness of the initial boundary value problem for degenerate hyperbolic systems with a localized term and its application to the linearized system for the motion of an inextensible hanging string [PDF]
Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems with a localized term and show its well-posedness in weighted Sobolev spaces.
arxiv