New explicit finite difference schemes for two‐dimensional diffusion subject to specification of mass

Noye, B. J.; Dehghan, Mohammad Sadegh

doi:10.1002/(sici)1098-2426(199907)15:4<521::aid-num7>3.3.co;2-i

Cited by 11 publications

(19 citation statements)

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“…which proves (7). From the properties of modi ed generalized Laguerre polynomials, it can be easily shown that,…”

Section: Some Properties Of Modi Ed Generalized Laguerre Polynomialsmentioning

confidence: 67%

“…Many di erential models in various research disciplines such as mathematics, uid dynamics, chemistry, biology, viscoelasticity, engineering and physics have arisen in semi-in nite domains [6][7][8][9][10]. Consequently, a lot of researchers have utilized various transformations on classical orthogonal polynomials to map the bounded interval [− , ] into [ , L] and [ , ∞) maintaining their orthogonal property.…”

Section: Introductionmentioning

confidence: 99%

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On the connection coefficients and recurrence relations arising from expansions in series of modified generalized Laguerre polynomials: Applications on a semi-infinite domain

Doha

Youssri

2019

Nonlinear Engineering

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Herein, three important theorems were stated and proved. The first relates the modified generalized Laguerre expansion coefficients of the derivatives of a function in terms of its original expansion coefficients; and an explicit expression for the derivatives of modified generalized Laguerre polynomials of any degree and for any order as a linear combination of modified generalized Laguerre polynomials themselves is also deduced. The second theorem gives new modified generalized Laguerre coefficients of the moments of one single modified generalized Laguerre polynomials of any degree. Finally, the third theorem expresses explicitly the modified generalized Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its modified generalized Laguerre coefficients. Some spectral applications of these theorems for solving ordinary differential equations with varying coefficients and some specific applied differential problems, by reducing them to recurrence relations in their expansion coefficients of the solution are considered.

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“…which proves (7). From the properties of modi ed generalized Laguerre polynomials, it can be easily shown that,…”

Section: Some Properties Of Modi Ed Generalized Laguerre Polynomialsmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

On the connection coefficients and recurrence relations arising from expansions in series of modified generalized Laguerre polynomials: Applications on a semi-infinite domain

Doha

Youssri

2019

Nonlinear Engineering

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“…1 From the table above, it could also be observed that the Method shows high computational strength as it compares favourably well with some known standard methods reported. 2 The superiority of the proposed methods could be established in the table above. From the table above, it could also be From table 6 above, it could also be observed that the Method shows some superiority in-terms of accuracy when compared with the method of Wang et al [11] and also compares favourably 3 (x, t) is the coordinate of x and t, u(x, t) is the exact solution, UM is the Upwind method, LM is the Lax method, Method represents the solution using the Method and Relative error=| u(x, t) -Method |/u(x, t).…”

Section: Tables Of Results and Comparisonmentioning

confidence: 99%

“…One of the most popular techniques applied to the solution of Advection equation is finite difference method [1,2]. In recent times, the finite element and the finite volume methods were also introduced.…”

Section: Introductionmentioning

confidence: 99%

A Class of Block Multi-derivative Numerical Techniques for Singular Advection Equations

Ogunniran

2024

J. Nig. Soc. Phys. Sci.

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The integration of some differential equations is hard to acquire because of the presence of singular point(s) in these equations. These equations are best solved by some unique technique. Multi-derivative techniques have a long history of powerful integration of such equations yet till date, a couple of class of this technique has been explored for integrating partial differential equations. This work centers around the development, analysis, and implementation of a class of multi-derivative technique on partial differential equations. The approaches were effectively analyzed and were turned out to be consistent, stable and convergent. Numerical outcomes got likewise demonstrated the approximation quality of the technique over existing techniques in the literature.

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“…Nonlinear problems play important roles in fluid mechanics and heat transfer. Except for a limited number of these problems, most of them do not have precise analytical solutions; therefore, these nonlinear equations should be solved using approximate semi-analytical and numerical solutions, such as the Adomian’s decomposition method (Sheikholeslami et al , 2013), difference transformation method (Sheikholeslami et al , 2016), homotopy perturbation method (Sheikholeslami and Ganji, 2014), exp-function method (Parand and Rad, 2012), control volume-based finite element method (Sheikholeslami et al , 2015; Sheikholeslami and Seyednezhad, 2018), finite difference method (Noye and Dehghan, 1999), finite element method (Bu et al , 2015; Sheikholeslami, 2017), meshfree methods (Rad et al , 2015a, 2015b) and spectral methods (Parand et al , 2013a, 2013b). Spectral methods have been successfully applied in the approximation of differential boundary value problems defined in semi-infinite domains.…”

Section: Introductionmentioning

confidence: 99%

An efficient numerical method to solve the Falkner-Skan problem over an isothermal moving wedge

Delkhosh

Parand

Ganji

2018

HFF

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Purpose This paper aims to solve the Falkner–Skan problem over an isothermal moving wedge using the combination of the quasilinearization method and the fractional order of rational Chebyshev function (FRC) collocation method on a semi-infinite domain. Design/methodology/approach The quasilinearization method converts the equation into a sequence of linear equations, and then by using the FRC collocation method, these linear equations are solved. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equation by similarity transformations. Findings The entropy generation and the effects of the various parameters of the problem are investigated, and various graphs for them are plotted. Originality/value Very good approximation solutions to the system of equations in the problem are obtained, and the convergence of numerical results is shown by using plots and tables.

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New explicit finite difference schemes for two‐dimensional diffusion subject to specification of mass

Cited by 11 publications

References 0 publications

On the connection coefficients and recurrence relations arising from expansions in series of modified generalized Laguerre polynomials: Applications on a semi-infinite domain

On the connection coefficients and recurrence relations arising from expansions in series of modified generalized Laguerre polynomials: Applications on a semi-infinite domain

A Class of Block Multi-derivative Numerical Techniques for Singular Advection Equations

An efficient numerical method to solve the Falkner-Skan problem over an isothermal moving wedge

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