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Numerical solution of Helmholtz equation by the modified Hopfield finite difference techniques

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/num.20019openalex-snapshot
On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation
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Identification of a time‐dependent coefficient in a partial differential equation subject to an extra measurement
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Numerical Methods for Partial Differential Equations
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Numerical Methods for Elliptic and Parabolic Partial Differential Equations
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“Neural” computation of decisions in optimization problems
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Neural algorithm for solving differential equations
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Terminal attractors for addressable memory in neural networks
inferredcites →https://doi.org/10.1016/0895-7177(94)90095-7openalex-snapshot
The numerical solution of linear ordinary differential equations by feedforward neural networks
inferredcites →https://doi.org/10.1016/0898-1221(90)90201-topenalex-snapshot
Numerical recipes in C—The art of scientific computing
inferredcites →https://doi.org/10.1016/j.chaos.2005.11.010openalex-snapshot
The one-dimensional heat equation subject to a boundary integral specification
inferredcites →https://doi.org/10.1016/j.matcom.2005.10.001openalex-snapshot
Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
inferredcites →https://doi.org/10.1016/j.mcm.2004.07.010openalex-snapshot
Parameter determination in a partial differential equation from the overspecified data
inferredcites →https://doi.org/10.1016/s0020-7225(01)00066-0openalex-snapshot
Fourth-order techniques for identifying a control parameter in the parabolic equations
inferredcites →https://doi.org/10.1016/s0045-7825(98)00023-1openalex-snapshot
High-order finite difference methods for the Helmholtz equation
inferredcites →https://doi.org/10.1016/s0096-3003(03)00305-9openalex-snapshot
Comparing numerical methods for Helmholtz equation model problem
inferredcites →https://doi.org/10.1016/s0168-9274(00)00057-xopenalex-snapshot
Determination of a control parameter in the two-dimensional diffusion equation
inferredcites →https://doi.org/10.1016/s0362-546x(00)00172-3openalex-snapshot
Fully explicit finite-difference methods for two-dimensional diffusion with an integral condition
inferredcites →https://doi.org/10.1016/s0377-0427(99)00065-5openalex-snapshot
Fully implicit finite differences methods for two-dimensional diffusion with a non-local boundary condition
inferredcites →https://doi.org/10.1016/s0893-6080(00)00013-7openalex-snapshot
Multilayer neural networks for solving a class of partial differential equations
inferredcites →https://doi.org/10.1016/s0893-6080(00)00095-2openalex-snapshot
Numerical solution of differential equations using multiquadric radial basis function networks
inferredcites →https://doi.org/10.1016/s0893-6080(03)00083-2openalex-snapshot
Numerical solution of elliptic partial differential equation using radial basis function neural networks
inferredcites →https://doi.org/10.1017/cbo9781139093590openalex-snapshot
Computational Fluid Dynamics for Engineers
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Neural networks and physical systems with emergent collective computational abilities.
inferredcites →https://doi.org/10.1073/pnas.81.10.3088openalex-snapshot
Neurons with graded response have collective computational properties like those of two-state neurons.
inferredcites →https://doi.org/10.1073/pnas.83.12.4263openalex-snapshot
Analog "neuronal" networks in early vision.
inferredcites →https://doi.org/10.1108/03684920710749857openalex-snapshot
Time‐splitting procedures for the solution of the two‐dimensional transport equation
inferredcites →https://doi.org/10.1109/20.376426openalex-snapshot
Direct solution method for finite element analysis using Hopfield neural network
inferredcites →https://doi.org/10.1109/72.712178openalex-snapshot
Artificial neural networks for solving ordinary and partial differential equations
inferredcites →https://doi.org/10.1109/72.870037openalex-snapshot
Neural-network methods for boundary value problems with irregular boundaries
inferredcites →https://doi.org/10.1109/ijcnn.2001.939059openalex-snapshot
A new implementation of discrete-time Hopfield net with higher capacity and speed of convergence
inferredcites →https://doi.org/10.1179/003962680791477326openalex-snapshot
APPLIED NUMERICAL ANALYSIS
inferredcites →https://doi.org/10.1364/ol.10.000098openalex-snapshot
Optical information processing based on an associative-memory model of neural nets with thresholding and feedback
inferredcites →https://doi.org/10.1364/ol.10.000163openalex-snapshot
Experimental comparison of the bandwidths of standard and dispersion-shifted fibers near their “zero-dispersion” wavelengths
inferredcites →https://doi.org/10.2307/2007712openalex-snapshot
Numerical Solution of Partial Differential Equations in Science and Engineering.
inferredcites →https://doi.org/10.2307/jj.12638999.13openalex-snapshot
Partial Differential Equations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1002/mma.3311openalex-snapshot
A regularization method for the cauchy problem of the modified Helmholtz equation
inferred← citeshttps://doi.org/10.1007/s00332-018-9525-3openalex-snapshot
Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations
inferred← citeshttps://doi.org/10.1007/s12040-023-02058-5openalex-snapshot
Prediction of significant wave height using machine learning and its application to extreme wave analysis
inferred← citeshttps://doi.org/10.1007/s12046-023-02083-6openalex-snapshot
Optimization of Hopfield Neural Network (HNN) using multiconnection and Lyapunov Energy Function (LEF) for storage and recall of handwritten images
inferred← citeshttps://doi.org/10.1007/s13201-019-0960-6openalex-snapshot
Phytoextraction capability of Azolla pinnata in the removal of rhodamine B from aqueous solution: artificial neural network and random forests approaches
inferred← citeshttps://doi.org/10.1016/j.amc.2019.03.042openalex-snapshot
A numerical scheme for solving a class of logarithmic integral equations arisen from two-dimensional Helmholtz equations using local thin plate splines
inferred← citeshttps://doi.org/10.1016/j.apm.2012.03.030openalex-snapshot
A Legendre spectral element method on a large spatial domain to solve the predator–prey system modeling interacting populations
inferred← citeshttps://doi.org/10.1016/j.cam.2023.115271openalex-snapshot
Model order reduction for parameterized electromagnetic problems using matrix decomposition and deep neural networks
inferred← citeshttps://doi.org/10.1016/j.enganabound.2025.106560openalex-snapshot
Dual integral formulation for acoustic resonances of a two-dimensional damped cavity with a thinpartition
inferred← citeshttps://doi.org/10.1016/j.fraope.2025.100332openalex-snapshot
An optimized hybrid block technique framework for partial differential equations by exploring radial basis function neural networks
inferred← citeshttps://doi.org/10.1016/j.thradv.2025.100022openalex-snapshot
Harnessing neural networks in hybrid block integrator for efficient solution of boundary value problems
inferred← citeshttps://doi.org/10.1080/00207160.2020.1819987openalex-snapshot
A kind of operator regularization method for Cauchy problem of the Helmholtz equation in a multi-dimensional case
inferred← citeshttps://doi.org/10.1080/10236198.2026.2734273openalex-snapshot
H-RBFs collocation method for solving the Helmholtz equation with variable coefficients
inferred← citeshttps://doi.org/10.1080/10798587.2008.10643243openalex-snapshot
Multi-Connect Architecture (MCA) Associative Memory: A Modified Hopfield Neural Network
inferred← citeshttps://doi.org/10.1142/s0219876218501293openalex-snapshot
A Complex Variable Boundary Element-Free Method for Potential and Helmholtz Problems in Three Dimensions
inferred← citeshttps://doi.org/10.1214/20-ejp423openalex-snapshot
Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
inferred← citeshttps://doi.org/10.3390/math10132207openalex-snapshot
Approximate Methods for Solving Problems of Mathematical Physics on Neural Hopfield Networks
inferred← citeshttps://doi.org/10.3390/math11244892openalex-snapshot
A Time-Fractional Parabolic Inequality on a Bounded Interval
inferred← citeshttps://doi.org/10.4018/ijfsa.296592openalex-snapshot
Optimization of Hopfield Neural Network for Improved Pattern Recall and Storage Using Lyapunov Energy Function and Hamming Distance
inferred← citeshttps://doi.org/10.4156/ijiip.vol2.issue1.6openalex-snapshot
MCA: A Developed Associative Memory Using Multi-Connect Architecture
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