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Partial differential equation

About: Partial differential equation is a research topic. Over the lifetime, 70811 publications have been published within this topic receiving 1626398 citations. The topic is also known as: PDE.


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Journal ArticleDOI
TL;DR: It is found that skin friction coefficient and couple stress coefficient reduces whereas heat transfer rate enhances when the micro-inertia parameter increases, and all the physical quantities get augmented with thermal radiation.
Abstract: This article investigates the behavior of conjugate natural convection over a finite vertical surface immersed in a micropolar fluid in the presence of intense thermal radiation. The governing boundary layer equations are made dimensionless and then transformed into suitable form by introducing the non-similarity transformations. The reduced system of parabolic partial differential equations is integrated numerically along the vertical plate by using an implicit finite difference Keller-box method. The features of fluid flow and heat transfer characteristics for various values of micropolar or material parameter, K , conjugate parameter, B , and thermal radiation parameter, R d , are analyzed and presented graphically. Results are presented for the local skin friction coefficient, heat transfer rate and couple stress coefficient for high Prandtl number. It is found that skin friction coefficient and couple stress coefficient reduces whereas heat transfer rate enhances when the micro-inertia parameter increases. All the physical quantities get augmented with thermal radiation.

37 citations

Journal ArticleDOI
TL;DR: The approach combines compact finite difference schemes that provide an inexpensive venue toward high-order accuracy with the method of difference potentials developed by Ryaben'kii, introducing a universal framework for treating boundary conditions of any type.
Abstract: We describe a high-order accurate methodology for the numerical simulation of time-harmonic waves governed by the Helmholtz equation. Our approach combines compact finite difference schemes that provide an inexpensive venue toward high-order accuracy with the method of difference potentials developed by Ryaben'kii. The latter can be interpreted as a generalized discrete version of the method of Calderon's operators in the theory of partial differential equations. The method of difference potentials can accommodate nonconforming boundaries on regular structured grids with no loss of accuracy due to staircasing. It introduces a universal framework for treating boundary conditions of any type. A significant advantage of this method is that changing the boundary condition within a fairly broad variety does not require any major changes to the algorithm and is computationally inexpensive. In this paper, we address various types of boundary conditions using the method of difference potentials. We demonstrate th...

37 citations

Journal Article
TL;DR: In this paper, sufficient conditions are established for the boundedness of all solutions of (1.1) and sufficient conditions for the limits of first and second order derivatives of the solutions of the solution tend to zero as t→∞.
Abstract: Sufficient conditions are established for the boundedness of all solutions of (1.1), and we also present some sufficient conditions, which ensure that the limits of first and second order derivatives of the solutions of (1.1) tend to zero as t→∞. Our results improve and include those results obtained by previous authors ([3], [5]).

37 citations

Journal ArticleDOI
TL;DR: An extended version of the "iterative secular equation" method was developed which implements direct Hellmann-Feynman theorem calculation of the partial derivatives of eigenvalues with respect to parameters of the Hamiltonian which are required for the fits.
Abstract: An improved three-dimensional potential energy surface for the H2–Kr system is determined from a direct fit of new infrared spectroscopic data for H2–Kr and D2–Kr to a potential energy function form based on the exchange-Coulomb model for the intermolecular interaction energy. These fits require repetitive, highly accurate simulations of the observed spectra, and both the strength of the potential energy anisotropy and the accuracy of the new data make the “secular equation perturbation theory” method used in previous analyses of H2–(rare gas) spectra inadequate for the present work. To address this problem, an extended version of the “iterative secular equation” method was developed which implements direct Hellmann–Feynman theorem calculation of the partial derivatives of eigenvalues with respect to parameters of the Hamiltonian which are required for the fits.

37 citations

01 Mar 1996
TL;DR: In this paper, the authors considered singular regenerate parabolic equations including the p-Laplace diffusion equation and established a comparison principle which is a natural extension of the paper by Ishii and Souganidis.
Abstract: We consider singular regenerate parabolic equations including the p-Laplace diffusion equation. We establish a comparison principle which is a natural extension of the paper by Ishii and Souganidis. Once we get a comparison principle we can construct the unique global-in-time viscosity solution to the Cauchy problem for the p-Laplace diffusion equation. The solution is founded, uniformly continuous in (0,T) x R{sup N} if tile initial data N is founded, uniformly continuous oil R{sup N}. 15 refs.

37 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20243
20231,153
20222,734
20213,040
20203,032
20192,781