An asymmetric backward problem for the inhomogeneous parabolic equation with time-dependent diffusivity

Minh, Triet Le; Hong, Phong Luu; Hoang, Quan Pham

doi:10.1007/s40314-017-0509-y

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…(2021), Azis (2022) and models with time-dependent coefficients, but with different aspects of study, in Luan and Khanh (2021), Geng et al . (2021), Minh et al . (2018), Hussein et al .…”

Section: Introductionmentioning

confidence: 99%

“…The computational study of several models for anisotropic media including functionally graded materials (FGMs) has attracted significant attention in recent years, and the development of these models has been a subject of intense research. Models with time-independent coefficients had been studied, for example, in AL-Bayati and Wrobel (2018), Ravnik and Tibuat (2019), Azis et al (2020, 2022), Abbaszadeh et al (2021, Azis (2022) and models with time-dependent coefficients, but with different aspects of study, in Luan and Khanh (2021), Geng et al (2021), Minh et al (2018), Hussein et al (2016), Van Bockstal and Slodi cka (2015), Lesnic et al (2013), Lesnic (2020, 2021), Sun et al (2019).…”

Section: Introductionmentioning

confidence: 99%

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A combined BEM and Laplace transform for unsteady modified-Helmholtz equation of time–space variable coefficients for anisotropic media

Azis

2023

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PurposeTwo-dimensional (2D) problems are governed by unsteady anisotropic modified-Helmholtz equation of time–space dependent coefficients are considered. The problems are transformed into a boundary-only integral equation which can be solved numerically using a standard boundary element method (BEM). Some examples are solved to show the validity of the analysis and examine the accuracy of the numerical method.Design/methodology/approach The 2D problems which are governed by unsteady anisotropic modified-Helmholtz equation of time–space dependent coefficients are solved using a combined BEM and Laplace transform. The time–space dependent coefficient equation is reduced to a time-dependent coefficient equation using an analytical transformation. Then, the time-dependent coefficient equation is Laplace transformed to get a constant coefficient equation, which can be written as a boundary-only integral equation. By utilizing a BEM, this integral equation is solved to find numerical solutions to the problems in the frame of the Laplace transform. These solutions are then inversely transformed numerically to obtain solutions in the original time–space frame.FindingsThe main finding of this research is the derivation of a boundary-only integral equation for the solutions of initial-boundary value problems governed by a modified-Helmholtz equation of time–space dependent coefficients for anisotropic functionally graded materials with time-dependent properties.Originality/valueThe originality of the research lies on the time dependency of properties of the functionally graded material under consideration.

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“…(2021), Azis (2022) and models with time-dependent coefficients, but with different aspects of study, in Luan and Khanh (2021), Geng et al . (2021), Minh et al . (2018), Hussein et al .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A combined BEM and Laplace transform for unsteady modified-Helmholtz equation of time–space variable coefficients for anisotropic media

Azis

2023

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A numerical investigation of unsteady space–time dependent coefficients anisotropic-diffusion convection reaction equation

Azis

2023

Engineering Analysis with Boundary Elements

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2D-xtDCR-LTBEM: A Fortran code for numerical solutions to the unsteady anisotropic-DCR equation of spatio-temporal coefficients

Azis

2023

SoftwareX

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An asymmetric backward problem for the inhomogeneous parabolic equation with time-dependent diffusivity

Cited by 4 publications

References 8 publications

A combined BEM and Laplace transform for unsteady modified-Helmholtz equation of time–space variable coefficients for anisotropic media

A combined BEM and Laplace transform for unsteady modified-Helmholtz equation of time–space variable coefficients for anisotropic media

A numerical investigation of unsteady space–time dependent coefficients anisotropic-diffusion convection reaction equation

2D-xtDCR-LTBEM: A Fortran code for numerical solutions to the unsteady anisotropic-DCR equation of spatio-temporal coefficients

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