𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Composite spectral method for solution of the diffusion equation with specification of energy

✍ Scribed by Mehdi Dehghan; Mehdi Ramezani

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
106 KB
Volume
24
Category
Article
ISSN
0749-159X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Many physical subjects are modeled by nonclassical parabolic boundary value problems with nonlocal boundary conditions replacing the classic boundary conditions. In this article, we introduce a new numerical method for solving the one‐dimensional parabolic equation with nonlocal boundary conditions. The approximate proposed method is based upon the composite spectral functions. The properties of composite spectral functions consisting of terms of orthogonal functions are presented and are utilized to reduce the problem to some algebraic equations. The method is easy to implement and yields very accurate result. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008

📜 SIMILAR VOLUMES

Formulations and analysis of the spectra
Formulations and analysis of the spectral volume method for the diffusion equation
✍ Sun, Yuzhi ;Wang, Z.J. 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 177 KB 👁 1 views

## Abstract The spectral volume (SV) method is a newly developed high‐order finite volume method for hyperbolic conservation laws on unstructured grids. It has been successfully demonstrated for multi‐dimensional Euler equations. We wish to extend the SV method to the Navier–Stokes equations. As a

A Composite Runge–Kutta Method for the S
A Composite Runge–Kutta Method for the Spectral Solution of Semilinear PDEs
✍ Tobin A. Driscoll 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 202 KB

A new composite Runge-Kutta (RK) method is proposed for semilinear partial differential equations such as Korteweg-de Vries, nonlinear Schrödinger, Kadomtsev-Petviashvili (KP), Kuramoto-Sivashinsky (KS), Cahn-Hilliard, and others having high-order derivatives in the linear term. The method uses Four

Overlapping Schwarz waveform relaxation
Overlapping Schwarz waveform relaxation method for the solution of the convection–diffusion equation
✍ Daoud S. Daoud 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 253 KB

## Abstract In this article we study the convergence of the overlapping Schwarz wave form relaxation method for solving the convection–diffusion equation over multi‐overlapped subdomains. It is shown that the method converges linearly and superlinearly over long and short time intervals, and the co

The method of fundamental solutions and
The method of fundamental solutions and quasi-Monte-Carlo method for diffusion equations
✍ C. S. Chen; M. A. Golberg; Y. C. Hon 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 131 KB 👁 2 views

The Laplace transform is applied to remove the time-dependent variable in the di usion equation. For nonharmonic initial conditions this gives rise to a non-homogeneous modiÿed Helmholtz equation which we solve by the method of fundamental solutions. To do this a particular solution must be obtained

A numerical method for the solution of t
A numerical method for the solution of the energy equation for steady turbulent heat transfer
✍ Mailand R. Strunk; Frank F. Tao 📂 Article 📅 1964 🏛 American Institute of Chemical Engineers 🌐 English ⚖ 509 KB

T = pressure, atm. u = collision diameter, A (a = azimuthal angle between the axes of the two di-(p(r) = Stockmayer potential, Equation (6) f i ( l J ) \* [ T ~] = reduced collision integral for the Lennardfi(2,2)\* [ T N ] = reduced collision integral for the Lennard-O ( l J ) \* [ TN, S o ] = redu

Iterative solution of systems of equatio
Iterative solution of systems of equations in the dual reciprocity boundary element method for the diffusion equation
✍ V. Bulgakov; B. Šarler; G. Kuhn 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 233 KB 👁 2 views

In this paper the diffusion equation is solved in two-dimensional geometry by the dual reciprocity boundary element method (DRBEM). It is structured by fully implicit discretization over time and by weighting with the fundamental solution of the Laplace equation. The resulting domain integral of the