Solution of Modified Equal Width Equation Using Quartic Trigonometric-Spline Method

Salih, Hamad; Tawfiq, L. N. M.

doi:10.1088/1742-6596/1664/1/012033

Cited by 11 publications

(7 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They are used to describe many life models such as exponential growth, population growth of species or the change in investment return over time 3 , cooling and heating problems, bank interest, radioactive decay problems even flow problems in solving continuous compound interest problems, orthogonal trajectories 4 and also involving fluid mechanics problems, population or conservation biology 5 , circuit design, heat transfer, seismic waves 6 . They are used in specific fields such as, in the field of medicine, where modeling cancer growth or the spread of disease may be described as differential equations 7 .…”

Section: Introductionmentioning

confidence: 99%

Efficient Approach for Solving (2+1) D- Differential Equations

Tawfiq,

Hussein

2023

Baghdad Sci.J

View full text Add to dashboard Cite

In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

show abstract

Section: Introductionmentioning

confidence: 99%

Efficient Approach for Solving (2+1) D- Differential Equations

Tawfiq,

Hussein

2023

Baghdad Sci.J

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…Many reliable methods have been discovered or developed to find the precise solutions of non-linear problems, among them the Hirota bilinear theory [4], Darboux transformation [5], the VIM [6,7], ADM [8,9], the HPM [10,11,12], parameter expansion method [13,14,15,16], HAM [17,18,19,20,21,22], spectral collocation method [23,24,25,26,27], and the Exp-function method [28,29,30,31,32,33].…”

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

View full text Add to dashboard Cite

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.

show abstract

Solution of Modified Equal Width Equation Using Quartic Trigonometric-Spline Method

Cited by 11 publications

References 12 publications

Efficient Approach for Solving (2+1) D- Differential Equations

Efficient Approach for Solving (2+1) D- Differential Equations

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

Contact Info

Product

Resources

About