Integral transform method

Cotta, Renato M.; Mikhailov, M.D.

doi:10.1016/0307-904x(93)90041-e

Cited by 42 publications

(23 citation statements)

References 3 publications

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“…iro et al, 2009;Cotta and Mikhailov, 1993;Cotta, 1994;Serfaty and Cotta, 1990;Naveira et al, 2007) and with the aid of Eqs. (5.10) and (5.11), Eq.…”

Section: Problem Solutionmentioning

confidence: 99%

“…The advantage of using the integral transform techniques is that it provides a systematic and straight-forward approach to the solution of a certain class of heat equations (Monteiro et al, 2009;Cotta and Mikhailov, 1993;Cotta, 1994;Serfaty and Cotta, 1990;Naveira et al, 2007). The method is particularly suitable for the solution of both homogeneous and nonhomogeneous boundary value problems of heat conduction.…”

Section: Introductionmentioning

confidence: 99%

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Generalization of the integral transform method to nonlinear heat-conduction problems in multilayered spherical media

Helal

2012

Journal of King Saud University - Science

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A method of solving heat conduction problems in multilayered spherical media is presented; it is based on producing an alternative formulation in which the inner layer of the composite sphere is lumped and the transient temperature distribution in the outer layer is obtained, in this, the nonlinear boundary conditions are treated as a source. The temperature distribution of the alternative formulation is then solved analytically. Different parametric studies are worked out and plotted to compare the two formulations for different values of Biot number and different thermal characteristic ratio with those obtained from a numerical solution developed using an explicit finite difference method, and to find the limiting criterion where breakdown of the approximation occurs.

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“…iro et al, 2009;Cotta and Mikhailov, 1993;Cotta, 1994;Serfaty and Cotta, 1990;Naveira et al, 2007) and with the aid of Eqs. (5.10) and (5.11), Eq.…”

Section: Problem Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalization of the integral transform method to nonlinear heat-conduction problems in multilayered spherical media

Helal

2012

Journal of King Saud University - Science

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“…Transform methods, applicable to porous media with properties that are uniform or vary in one dimension, have been used to produce a variety of semianalytic solutions. These include the direct application of the Laplace transform [Yates, 1990;Xu and Brusseau, 1996;Shan and Javandel, 1997;Sim and Chrysikopoulos, 1999;Moridis, 2002] as well as extensions, such as the generalized integral transform technique (GITT) [Mikhailov and € Ozisik, 1984;Cotta, 1992;Cotta and Mikhailov, 1993;Guerrero and Skaggs, 2010]. There are also asymptotic methods for layered media [Gelhar and Collins, 1971].…”

Section: Introductionmentioning

confidence: 99%

Trajectory‐based modeling of fluid transport in a medium with smoothly varying heterogeneity

Vasco

Pride

Commer

2016

Water Resources Research

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Using an asymptotic methodology, valid in the presence of smoothly varying heterogeneity and prescribed boundaries, we derive a trajectory-based solution for tracer transport. The analysis produces a Hamilton-Jacobi partial differential equation for the phase of the propagating tracer front. The trajectories follow from the characteristic equations that are equivalent to the Hamilton-Jacobi equation. The paths are determined by the fluid velocity field, the total porosity, and the dispersion tensor. Due to their dependence upon the local hydrodynamic dispersion, they differ from conventional streamlines. This difference is borne out in numerical calculations for both uniform and dipole flow fields. In an application to the computational X-ray imaging of a saline tracer test, we illustrate that the trajectories may serve as the basis for a form of tracer tomography. In particular, we use the onset time of a change in attenuation for each volume element of the X-ray image as a measure of the arrival time of the saline tracer. The arrival times are used to image the spatial variation of the effective hydraulic conductivity within the laboratory sample.

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“…Transform is an important method to solve mathematical problems. Many useful transforms for solving various problems were appeared in open literature, such as the travelling wave transform [30] , the Laplace transform [31], the Fourier transform [32], the Bücklund transformation [33], the integral transform [34], and the local fractional integral transforms [35]. Very recently the fractional complex transform [36, 37, 38, 39] was suggested to convert fractional order differential equations with modified Riemann-Liouville derivatives into integer order differential equations, and the resultant equations can be solved by advanced calculus.…”

Section: Introductionmentioning

confidence: 99%

Solutions of fractional Zakharov-Kuznetsov equations by fractional complex transform

Yulita¹,

Batiha²,

Shatnawi³

2016

IJAMR

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In this paper, fractional complex transform (FCT) with help of variational iteration method (VIM) is used to obtain numerical and analytical solutions for the fractional Zakharov-Kuznetsov equations. Fractional complex transform (FCT) is proposed to convert fractional Zakharov-Kuznetsov equations to its differential partner and then applied VIM to the new obtained equations. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.

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Integral transform method

Cited by 42 publications

References 3 publications

Generalization of the integral transform method to nonlinear heat-conduction problems in multilayered spherical media

Generalization of the integral transform method to nonlinear heat-conduction problems in multilayered spherical media

Trajectory‐based modeling of fluid transport in a medium with smoothly varying heterogeneity

Solutions of fractional Zakharov-Kuznetsov equations by fractional complex transform

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