Spreadsheet solution of hyperbolic partial differential equations [for EM field calculations]

Kharab, Abdelwahab; Kharab, Rachid

doi:10.1109/13.554675

Cited by 6 publications

(2 citation statements)

References 7 publications

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“…We carry forward our strategy for resolving wave equations by utilizing two patterns of Bernstein neural networks. Let us take into consideration the Cauchy problem (5), where the solution v relies on both spatial as well as temporal variables and respectively. The trial solution associated with (5)…”

Section: Controller Design With Bernstein Neural Network Approximationmentioning

confidence: 99%

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Solving Partial Differential Equations with Bernstein Neural Networks

Razvarz

Jafari

Gegov

2018

Advances in Intelligent Systems and Computing

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In this paper, a neural network-based procedure is suggested to produce estimated solutions (controllers) for the second-order nonlinear partial differential equations (PDEs). This concept is laid down so as to produce a prevalent approximation on the basis of the learning method which is at par with quasi-Newton rule. The proposed neural network contains the regularizing parameters (weights and biases), that can be utilized for making the error function least. Besides, an advanced technique is presented for resolving PDEs based on the usage of Bernstein polynomial. Numerical experiments alongside comparisons show the fantastic capacity of the proposed techniques.

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Section: Controller Design With Bernstein Neural Network Approximationmentioning

confidence: 99%

“…In the following, some numerical solutions are laid down that have been suggested by other researchers. In [5], implementation of a spreadsheet program produces the numerical solution of the hyperbolic equation. Some researchers also generate an array solution that includes the value of the solution at a selected group of points [6].…”

Section: Introductionmentioning

confidence: 99%