A new spectral Jacobi–Gauss–Lobatto collocation (J–GL–C) method is developed and analyzed to solve numerically parabolic partial differential equations (PPDEs) subject to initial and nonlocal boundary conditions. The method depends basically on the fact that an expansion in a series of Jacobi polynomials is assumed, for the function and its space derivatives occurring in the partial differential equation (PDE), the expansion coefficients are then determined by reducing the PDE with its boundary conditions into a system of ordinary differential equations (SODEs) for these coefficients. This system may be solved numerically in a step-by-step manner by using implicit the Runge–Kutta (IRK) method of order four. The proposed method, in contrast to common finite-difference and finite-element methods, has the exponential rate of convergence for the spatial discretizations. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented.
Skip Nav Destination
Article navigation
March 2015
Research-Article
An Accurate Jacobi Pseudospectral Algorithm for Parabolic Partial Differential Equations With Nonlocal Boundary Conditions
E. H. Doha,
E. H. Doha
Department of Mathematics,
Faculty of Science,
e-mail: eiddoha@frcu.eun.eg
Faculty of Science,
Cairo University
,Giza 12613
, Egypt
e-mail: eiddoha@frcu.eun.eg
Search for other works by this author on:
A. H. Bhrawy,
A. H. Bhrawy
Department of Mathematics,
Faculty of Science,
Faculty of Science,
King Abdulaziz University
,Jeddah 21589
, Saudi Arabia
Department of Mathematics,
Faculty of Science,
e-mail: alibhrawy@yahoo.co.uk
Faculty of Science,
Beni-Suef University
,Beni-Suef 62511
, Egypt
e-mail: alibhrawy@yahoo.co.uk
Search for other works by this author on:
M. A. Abdelkawy
M. A. Abdelkawy
Department of Mathematics,
Faculty of Science,
e-mail: melkawy@yahoo.com
Faculty of Science,
Beni-Suef University
,Beni-Suef 62511
, Egypt
e-mail: melkawy@yahoo.com
Search for other works by this author on:
E. H. Doha
Department of Mathematics,
Faculty of Science,
e-mail: eiddoha@frcu.eun.eg
Faculty of Science,
Cairo University
,Giza 12613
, Egypt
e-mail: eiddoha@frcu.eun.eg
A. H. Bhrawy
Department of Mathematics,
Faculty of Science,
Faculty of Science,
King Abdulaziz University
,Jeddah 21589
, Saudi Arabia
Department of Mathematics,
Faculty of Science,
e-mail: alibhrawy@yahoo.co.uk
Faculty of Science,
Beni-Suef University
,Beni-Suef 62511
, Egypt
e-mail: alibhrawy@yahoo.co.uk
M. A. Abdelkawy
Department of Mathematics,
Faculty of Science,
e-mail: melkawy@yahoo.com
Faculty of Science,
Beni-Suef University
,Beni-Suef 62511
, Egypt
e-mail: melkawy@yahoo.com
Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received December 30, 2013; final manuscript received February 20, 2014; published online January 12, 2015. Assoc. Editor: Ahmet S. Yigit.
J. Comput. Nonlinear Dynam. Mar 2015, 10(2): 021016 (13 pages)
Published Online: March 1, 2015
Article history
Received:
December 30, 2013
Revision Received:
February 20, 2014
Online:
January 12, 2015
Citation
Doha, E. H., Bhrawy, A. H., and Abdelkawy, M. A. (March 1, 2015). "An Accurate Jacobi Pseudospectral Algorithm for Parabolic Partial Differential Equations With Nonlocal Boundary Conditions." ASME. J. Comput. Nonlinear Dynam. March 2015; 10(2): 021016. https://doi.org/10.1115/1.4026930
Download citation file:
Get Email Alerts
Irrational Nonlinearity Enhances the Targeted Energy Transfer in a Rotary Nonlinear Energy Sink
J. Comput. Nonlinear Dynam (June 2024)
Investigation of Gear Meshing Vibration and Meshing Impact Resonance Intensity Assessment
J. Comput. Nonlinear Dynam (May 2024)
Hand Vibration Reduction Using Nonlinear Vibration Absorber for the Vibro-Impact Hammer Model
J. Comput. Nonlinear Dynam
Related Articles
Analysis of Laminated Anisotropic Cylindrical Shell by Chebyshev Collocation Method
J. Appl. Mech (May,2003)
On a Numerical Approach to Solve Multi-Order Fractional Differential Equations With Initial/Boundary Conditions
J. Comput. Nonlinear Dynam (November,2015)
Finite Element Solution of Boundary Value Problems: Theory and Computation. Classics in Applied Math, Vol. 35
Appl. Mech. Rev (May,2002)
Compatibility Equations in the Theory of Elasticity
J. Vib. Acoust (April,2003)
Related Proceedings Papers
Related Chapters
Scalable Video Streaming Multicast of Multiple Groups over Broadband Wireless Networks
International Conference on Computer Engineering and Technology, 3rd (ICCET 2011)
Introduction
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow
Modeling of SAMG Operator Actions in Level 2 PSA (PSAM-0164)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)