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Computation of the Complex Error Function Using Modified Trapezoidal Rules [PDF]

SIAM Journal on Numerical Analysis, 2021
In this paper we propose a method for computing the Faddeeva function $w(z) := e^{-z^2}\mathrm{erfc}(-i z)$ via truncated modified trapezoidal rule approximations to integrals on the real line. Our starting point is the method due to Matta and Reichel (Math. Comp. 25 (1971), pp. 339-344) and Hunter and Regan (Math. Comp. 26 (1972), pp.
Simon Chandler-Wilde
exaly   +5 more sources

Approximation of the modified error function [PDF]

Applied Mathematics and Computation, 2018
In this article, we obtain explicit approximations of the modified error function introduced in Cho, Sunderland. Journal of Heat Transfer 96-2 (1974), 214-217, as part of a Stefan problem with a temperature-dependent thermal conductivity. This function depends on a parameter $δ$, which is related to the thermal conductivity in the original phase-change
Domingo A Tarzia, Natalia Nieves Salva, Andrea N Ceretani   +2 more
exaly   +8 more sources

Existence and uniqueness of the p-generalized modified error function

Electronic Journal of Differential Equations, 2020
In this article, we define a p-generalized modified error function as the solution to a non-linear ordinary differential equation of second order, with a Robin type boundary condition at x=0.
Julieta Bollati, Jose A. Semitiel, Maria F. Natale, Domingo A. Tarzia   +3 more
doaj   +5 more sources

Improving the error backpropagation algorithm with a modified error function [PDF]

IEEE Transactions on Neural Networks, 1997
This letter proposes a modified error function to improve the error backpropagation (EBP) algorithm of multilayer perceptrons (MLPs) which suffers from slow learning speed. To accelerate the learning speed of the EBP algorithm, the proposed method reduces the probability that output nodes are near the wrong extreme value of sigmoid activation function.
Sang-Hoon Oh
exaly   +4 more sources

Modified Neural Network with Hysteresis Operators and Adaptive Learning for Tracking Control of Piezoelectric Stack Actuator [PDF]

Micromachines
According to the proposed four-layer modified neural network with adaptive learning, an adaptive learning model is designed, and the Play operator weight function update algorithm, the dead-zone operator weight function update algorithm, and the hybrid ...
Yuansheng Chen, Wenwu Yang, Lei Yuan, Shaona Liu, Ruijing Zhang, Xinggan Lu, Wei Chen   +6 more
doaj   +2 more sources

Existence and uniqueness of the modified error function

Applied Mathematics Letters, 2017
This article is devoted to prove the existence and uniqueness of solution to the non-linear second order differential problem through which is defined the modified error function introduced in Cho-Sunderland, J. Heat Transfer, 96-2:214-217, 1974. We prove here that there exists a unique non-negative analytic solution for small positive values of the ...
Domingo A Tarzia, Natalia Nieves Salva, Andrea N Ceretani   +2 more
exaly   +7 more sources

Measurement Error Estimation for Distributed Smart Meters Through a Modified BP Neural Network

Frontiers in Energy Research, 2022
Smart meters generally suffer degradation of metering accuracy and performance due to aging, faults, and other factors, which, however, are difficult to detect.
Tian Xia, Cencen Liu, Ming Lei, Shuibin Xia, Ding Li, Dongyue Ming   +5 more
doaj   +3 more sources

Simple neuro-controller with a modified error function for a synchronous generator

International Journal of Electrical Power and Energy Systems, 2003
A simple neuro-controller for a synchronous generator is presented in this paper. The controller consists of a single neuron trained on-line using the back propagation algorithm based on a modified error function. The modified error function uses the controlled variable and its derivatives.
A M Zaki, O A Mahgoub, M M Salem
exaly   +2 more sources

A Nonclassical Stefan Problem with Nonlinear Thermal Parameters of General Order and Heat Source Term

Axioms, 2023
The analytic solution for a general form of the Stefan problem with nonlinear temperature-dependent thermal parameters and a heat source the term is obtained.
Ammar Khanfer, Lazhar Bougoffa, Smail Bougouffa   +2 more
doaj   +1 more source

A Modified RBF Collocation Method for Solving the Convection-Diffusion Problems

Abstract and Applied Analysis, 2023
The main purposes of this study are to propose the modified radial basis function (RBF) collocation method using a hybrid radial basis function to solve the convection-diffusion problems numerically and to choose the optimal shape parameter of radial ...
Nissaya Chuathong
doaj   +1 more source