Higher-Order Numerical Scheme for the Fractional Heat Equation with Dirichlet and Neumann Boundary Conditions

Download

index.pdf

Date

2013-06-01

Author

Priya, G. Sudha
Prakash, P.
Nieto, J. J.
Kayar, Z.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

274
views

0
downloads

In this article, we consider a higher-order numerical scheme for the fractional heat equation with Dirichlet and Neumann boundary conditions. By using a fourth-order compact finite-difference scheme for the spatial variable, we transform the fractional heat equation into a system of ordinary fractional differential equations which can be expressed in integral form. Further, the integral equation is transformed into a difference equation by a modified trapezoidal rule. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm.

Subject Keywords

Modelling and Simulation, Mechanics of Materials, Condensed Matter Physics, Numerical Analysis, Computer Science Applications

URI

https://hdl.handle.net/11511/67362

Journal

NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS

DOI

https://doi.org/10.1080/10407790.2013.778719

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Modelling and Monte Carlo simulation of the atomic ordering processes in Ni3Al intermetallics Mehrabov, Amdulla; Akdeniz, Mahmut Vedat (IOP Publishing, 2007-03-01) The evolution of atomic ordering processes in Ni3Al has been modelled by a Monte Carlo ( MC) simulation method combined with the electronic theory of alloys in pseudopotential approximation. The magnitudes of atomic ordering energies of atomic pairs in the Ni3Al system have been calculated by means of electronic theory in pseudopotential approximation up to the 4th coordination spheres and subsequently used as input data for MC simulation for more detailed analysis for the first time. The Bragg - Williams l...
Annulus criteria for mixed nonlinear elliptic differential equations ŞAHİNER, YETER; Zafer, Ağacık (Elsevier BV, 2011-05-01) New oscillation criteria are obtained for forced second order elliptic partial differential equations with damping and mixed nonlinearities of the form
Nonlocal hydrodynamic type of equations Gürses, Metin; Pekcan, Asli; Zheltukhın, Kostyantyn (Elsevier BV, 2020-06-01) We show that the integrable equations of hydrodynamic type admit nonlocal reductions. We first construct such reductions for a general Lax equation and then give several examples. The reduced nonlocal equations are of hydrodynamic type and integrable. They admit Lax representations and hence possess infinitely many conserved quantities.
Simulation of dissolution of silicon in an indium solution by spectral methods Coskun, AU; Yener, Y; Arinc, F (IOP Publishing, 2002-09-01) The results of a numerical simulation of natural convection due to concentration gradients during dissolution of silicon in an indium solution in a horizontal substrate-solution-substrate system are presented. The Chebyshev-Tau spectral method has been used for the simulations. The results are in very good agreement with the experimental data available in the literature. It is concluded that the discrepancies in the dissolution depths between the previous simulations and experimental data, especially at the...
Periodic solutions of the hybrid system with small parameter Akhmet, Marat; Ergenc, T. (Elsevier BV, 2008-06-01) In this paper we investigate the existence and stability of the periodic solutions of a quasilinear differential equation with piecewise constant argument. The continuous and differentiable dependence of the solutions on the parameter and the initial value is considered. A new Gronwall-Bellman type lemma is proved. Appropriate examples are constructed.

Citation Formats

G. S. Priya, P. Prakash, J. J. Nieto, and Z. Kayar, “Higher-Order Numerical Scheme for the Fractional Heat Equation with Dirichlet and Neumann Boundary Conditions,” NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS, pp. 540–559, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/67362.