Hybrid evolutionary padé approximation approach for numerical treatment of nonlinear partial differential equations

Nisar, Kottakkaran Sooppy; Ali, Javaid; Mahmood, Muhammad Khalid; Ahmad, Daud; Ali, Shahbaz

doi:10.1016/j.aej.2021.03.030

Cited by 24 publications

(12 citation statements)

References 30 publications

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“…Modeling differential equations as equivalent optimization problems [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] is one of the most modern techniques to obtain reliable solutions, especially when the traditional method lacks handling one or more aspects of the physical phenomena. The related examples of such modeling include solving nonlinear ordinary differential equations, inverse partial differential equations, and epidemiological models.…”

Section: Literature Surveymentioning

confidence: 99%

“…The related examples of such modeling include solving nonlinear ordinary differential equations, inverse partial differential equations, and epidemiological models. Ali et al [ 37 , 38 ] proposed a novel evolutionary Padé approximation (EPA) scheme for solving epidemiological models and nonlinear partial differential equations. Padé rational approximation functions are a vital research area due to their tremendous applications in several scientific areas [ 39 , 40 ].…”

Section: Literature Surveymentioning

confidence: 99%

“…This work presents the first EPA scheme-based formulation and solution of the Covid-19 disease dynamical model with crowding effect as an optimization problem to the best of our knowledge. In the original proposal [ 37 , 38 ] of the EPA scheme, the focus on optimization was minimal, and the underlying model was comparatively less complex. But the present study adds some new aspects to the theory of the EPA scheme for solving epidemiological models with crowding effect.…”

Section: Literature Surveymentioning

confidence: 99%

“…For any

, let

and

denote polynomial functions of variable

having degrees

and

, respectively. Then Padé rational approximation functions of orders

[ 37 , 38 ] for state variables are:

Here

and

are polynomial functions with real coefficients

for each

defined by:

The derivative of

with respect to

can be expressed as under:

Formation of residual functions …”

Section: Evolutionary Padé Approximation (Epa) Scheme For Covid-19 Modelmentioning

confidence: 99%

See 3 more Smart Citations

Evolutionary optimized Padé approximation scheme for analysis of covid-19 model with crowding effect

Ali¹,

Raza

Ahmed

et al. 2021

Operations Research Perspectives

Self Cite

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Section: Literature Surveymentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

Section: Literature Surveymentioning

confidence: 99%

“…For any

, let

and

denote polynomial functions of variable

having degrees

and

, respectively. Then Padé rational approximation functions of orders

[ 37 , 38 ] for state variables are:

Here

and

are polynomial functions with real coefficients

for each

defined by:

The derivative of

with respect to

can be expressed as under:

Formation of residual functions …”

Section: Evolutionary Padé Approximation (Epa) Scheme For Covid-19 Modelmentioning

confidence: 99%

See 2 more Smart Citations

Evolutionary optimized Padé approximation scheme for analysis of covid-19 model with crowding effect

Ali¹,

Raza

Ahmed

et al. 2021

Operations Research Perspectives

Self Cite

View full text Add to dashboard Cite

“…The roles which Nonlinear Partial Differential Equations (NPDEs) play are prominent in the description and analysis of real-life processes and phenomena (See e.g., [1,2]). Therefore, it is pivotal to seek for the ways of obtaining exact solutions of NPDEs for a proper and accurate analysis.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of nonlinear delay reaction-diffusion equations with variable coefficients

Aibinu,

Thakur,

Moyo

2021

Preprint

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A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized form of nonlinear equations of reaction-diffusion type with delay and which are nonlinear and associated with variable coefficients. A novel technique is used in this study to obtain the exact solutions which are new and are of the form of traveling-wave solutions. Arbitrary functions are present in the solutions and they also contain free parameters, which make them suitable for usage in solving certain modeling problems, testing numerical and approximate analytical methods. The results of this study also find applications in obtaining the exact solutions of other forms of partial differential equations which are more complex. Specific examples of nonlinear equations of reaction-diffusion type with delay are given and their exact solutions are presented. Solutions of certain reaction-diffusion equations are also displayed graphically.

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Fractional dynamics of entropy generation in unsteady mixed convection of a reacting nanofluid over a slippery permeable plate in Darcy–Forchheimer porous medium

Makinde,

Khan,

Trounev

et al. 2024

Z Angew Math Mech

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This paper presents a theoretical investigation of the inherent irreversibility in unsteady fractional time derivative mixed convection of a reacting nanofluid with heat and mass transfer mechanism over a slippery permeable plate embedded in a Darcy–Forchheimer porous medium. The model fractional partial differential equations are obtained based on conservation laws and numerically solved using the implicit finite difference scheme. The study displays and discusses the effects of various emerging parameters on the overall flow structure, such as velocity profiles, temperature distribution, nanoparticles concentration profiles, skin friction, Nusselt number, Sherwood number, entropy generation rate, and Bejan number. It was found that an increase in dimensionless time and fractional parameters leads to a decrease in both the entropy generation rate and the Bejan number. The study revealed that fractional order derivatives can capture intrinsic memory effects, non‐local behaviour, and anomalous diffusion in the nanofluid flow process. This can ultimately lead to better engineering system design and control.

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Hybrid evolutionary padé approximation approach for numerical treatment of nonlinear partial differential equations

Cited by 24 publications

References 30 publications

Evolutionary optimized Padé approximation scheme for analysis of covid-19 model with crowding effect

Evolutionary optimized Padé approximation scheme for analysis of covid-19 model with crowding effect

Exact solutions of nonlinear delay reaction-diffusion equations with variable coefficients

Fractional dynamics of entropy generation in unsteady mixed convection of a reacting nanofluid over a slippery permeable plate in Darcy–Forchheimer porous medium

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