On the stable computational, semi-analytical, and numerical solutions of the Langmuir waves in an ionized plasma

Khater, Mostafa M. A.; Attia, Raghda A. M.; Qin, Haiyong; Kadry, Heba; Kharabsheh, Radwan; Lu, Dianchen

doi:10.3233/jifs-179569

Cited by 3 publications

(2 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Implementing the following numerical schemes (Adomian decomposition [AD], El Kalla [EK], cubic B-Spline [CBS], extended cubic B-spline [ECBS], exponential cubic B-spline [ExCBS]) listed above for evaluating the numerical scheme of [30][31][32][33][34] of the nonlinear predator-prey (PP) system that is given by [35,36]…”

Section: Introductionmentioning

confidence: 99%

“…Implementing the following numerical schemes (Adomian decomposition [AD], El Kalla [EK], cubic B‐Spline [CBS], extended cubic B‐spline [ECBS], exponential cubic B‐spline [ExCBS]) listed above for evaluating the numerical scheme of [30–34] of the nonlinear predator–prey (PP) system that is given by [35, 36]

\{\begin{matrix} leftlmatrix \\ {scriptQ}_{t} = {scriptQ}_{italicxx} - β Q + false(1 + β false) {scriptQ}^{2} - {scriptQ}^{3} - Q F, \\ {scriptF}_{t} = {scriptF}_{italicxx} + k Q F - m F - δ {scriptF}^{3}, \end{matrix}

where k , δ , m , β are positive arbitrary parameters to be determined later. The diffusive PP model dynamics have taken on the following parameter relationships, namely

[m = β & k + \frac{1}{\sqrt{δ}} - m = 1]

.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulations for the predator–prey model as a prototype of an excitable system

Khater

Almohsen

Băleanu

2020

Numerical Methods Partial

View full text Add to dashboard Cite

This research paper investigates the numerical solutions of the predator–prey model through five recent numerical schemes (Adomian decomposition, El Kalla, cubic B‐spline, extended cubic B‐spline, exponential cubic B‐spline). We investigate the obtained computational solutions via the modified Khater methods. This model is considered as a well‐known bimathematical model to describe the prototype of an excitable system. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. The accuracy of the obtained numerical solutions is investigated by calculating the absolute error between the exact and numerical solutions. Many sketches are given to illustrate the matching between the exact and numerical solutions.

show abstract

Section: Introductionmentioning

confidence: 99%

\{\begin{matrix} leftlmatrix \\ {scriptQ}_{t} = {scriptQ}_{italicxx} - β Q + false(1 + β false) {scriptQ}^{2} - {scriptQ}^{3} - Q F, \\ {scriptF}_{t} = {scriptF}_{italicxx} + k Q F - m F - δ {scriptF}^{3}, \end{matrix}

where k , δ , m , β are positive arbitrary parameters to be determined later. The diffusive PP model dynamics have taken on the following parameter relationships, namely

[m = β & k + \frac{1}{\sqrt{δ}} - m = 1]

.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations for the predator–prey model as a prototype of an excitable system

Khater

Almohsen

Băleanu

2020

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

Novel exact solutions of the fractional Bogoyavlensky–Konopelchenko equation involving the Atangana-Baleanu-Riemann derivative

Khater

Ghanbari

Nisar

et al. 2020

Alexandria Engineering Journal

View full text Add to dashboard Cite

Variational Principle and Approximate Solution for the Fractal Generalized Benjamin–bona–mahony–burgers Equation in Fluid Mechanics

Wang

2021

Fractals

View full text Add to dashboard Cite

The well-known generalized Benjamin–Bona–Mahony–Burgers (gBBMB) equation is widely used in the fluid mechanics, but it becomes invalid under the non-smooth boundary. So this paper, for the first time ever, extends the gBBMB equation into the fractal form that still works under the non-smooth boundary. By using the semi-inverse method, we develop the fractal variational formulations for the problem, which can provide the conservation laws in an energy form, and reveal the possible solution structures of the equation. Furthermore, the two-scale transform method combined with the variational iteration method is used to solve the fractal gBBMB equation. The obtained results show a good agreement with the existed results.

show abstract

On the stable computational, semi-analytical, and numerical solutions of the Langmuir waves in an ionized plasma

Cited by 3 publications

References 40 publications

Numerical simulations for the predator–prey model as a prototype of an excitable system

Numerical simulations for the predator–prey model as a prototype of an excitable system

Novel exact solutions of the fractional Bogoyavlensky–Konopelchenko equation involving the Atangana-Baleanu-Riemann derivative

Variational Principle and Approximate Solution for the Fractal Generalized Benjamin–bona–mahony–burgers Equation in Fluid Mechanics

Contact Info

Product

Resources

About