Efficient approach for solving high order (2+1)D-differential equation

Hussein, Noor; Tawfiq, L. N. M.

doi:10.1063/5.0093671

Cited by 6 publications

(5 citation statements)

References 24 publications

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“…. In [13], Yamashita and Fukushima proved the convergence is quadratic of the LM method when choosing µ k = E k 2 , based on the properties of an unconstrained optimization. Herein, first we prove the NLM method has super linear convergence if we choose µ k = E k δ , then, depending on the properties of singular value decomposition (SVD) of the Jacobian matrix, we get the quadratic convergence.…”

Section: Hypothesismentioning

confidence: 99%

“…Herein, artificial neural networks techniques have been proposed for the following problem. During the last several decades, there has been a lot of interest research of various machine intelligence approaches, particularly artificial neural networks (ANNs) is used to solve differential equations [13,42,50]. Because ANNs are known to have universal approximation capabilities [19], parallel processing technique, when compared to other traditional numerical approaches.…”

Section: Introductionmentioning

confidence: 99%

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Design an efficient neural network for solving steady state problems

Thirthar,

Tawfiq,

Shah

et al. 2024

J. Math. Computer Sci.

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Section: Hypothesismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design an efficient neural network for solving steady state problems

Thirthar,

Tawfiq,

Shah

et al. 2024

J. Math. Computer Sci.

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“…A mathematical model is a condensed, mathematically stated depiction of physical reality [1]. Nonlinear PDEs are also crucial for study in a wide range of domains, including hydrodynamics, engineering, quantum field theory, optics, plasma physics, etc [2,3]. Non-linear high order PDEs have an important role in representing different applied science such physical or chemical phenomena arising in engineering [4].…”

Section: Introductionmentioning

confidence: 99%

Novel Neural Network Based on New Modification of BFGS Update Algorithm for Solving Partial Differential Equations

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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In this article, an effective neural network is created using unconstrained optimization the brand-new BFGS training algorithm. The fourth order nonlinear partial differential equation is mathematically modeled with feed-forward artificial neural network with some adaptive parameters. The network is trained by new modification of BFGS method to avoid some troubles occurs when the network trained by current BFGS. The conventional updated Hessian approximations approach needed significant memory, storage, and cost computing for each iteration. One of these update's novel features is its ability to estimate the 2 nd order curvature of the goal function (energy functions) with high order precision while using the provided gradient and function value data. It is shown that the global convergence properties of the suggested modification, there is a parameter ρ in the update formulae which ranges from zero to one. The numerical experiments demonstrate that the improved BFGS update will be more accurate and more effective than the traditional BFGS methods. The proposed algorithm has well properties such: it has global convergence for energy function which is convex functions; also to get optimal step length we used a nonmonotone line search technique to modify the effectiveness of the proposed algorithm. Finally, used suggested training algorithm, to learned an appropriate neural network for accurately solving any non-linear PDEs.

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“…Nonlinear phenomena hold significant importance across various scientific disciplines, notably in plasma waves, solid-state physics, fluid, plasma physics, mechanics, and chemical Email address: luma.n.m@ihcoedu.uobaghdad.edu.iq (Luma N. M. T awfiq) physics. The investigation of precise and numerical solutions, particularly those pertaining to travelling wave phenomena in nonlinear equations with in the field of mathematical physics, holds significant in soliton theory [2,3].…”

Section: Introductionmentioning

confidence: 99%

Solving (3+1) D- New Hirota Bilinear Equation Using Tanh Method and New Modification of Extended Tanh Method

2023

Advances in the Theory of Nonlinear Analysis and Its Application

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In this article Tanh method is considered as effective approach to get solutions of some types of non-linear partial differential equations. Then we suggested new modification for extended Tanh method as highly effective approach to obtaining precise traveling wave solutions to these types of equations. Then using both methods, to solve the (3+1) D-new Hirote bilinear equation (NHBE) and then we compare between the results to illustrate the effectiveness of suggested modification. The interpretation of these solutions presented graphical to illustrate behaviors of the solutions gives us some popular shapes include solutions of type solitary wave, the singular wave, the kink wave, and the singular kink wave.

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Efficient approach for solving high order (2+1)D-differential equation

Cited by 6 publications

References 24 publications

Design an efficient neural network for solving steady state problems

Design an efficient neural network for solving steady state problems

Novel Neural Network Based on New Modification of BFGS Update Algorithm for Solving Partial Differential Equations

Solving (3+1) D- New Hirota Bilinear Equation Using Tanh Method and New Modification of Extended Tanh Method

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