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Title: High-accuracy cubic spline alternating group explicit methods for 1D quasi-linear parabolic equations
Authors: Mohanty R.K.
Jain, Manoj Kumar
Published in: International Journal of Computer Mathematics
Abstract: In this article, we study the application of the alternating group explicit (AGE) and Newton-AGE iterative methods to a two-level implicit cubic spline formula of O(k2+kh2+h4) for the solution of 1D quasi-linear parabolic equation uxx = φ (x, t, u, ux, ut), 0 < x < 1, t > 0 subject to appropriate initial and natural boundary conditions prescribed, where k > 0 and h > 0 are mesh sizes in t- and x-directions, respectively. The proposed cubic spline methods require 3-spatial grid points and are applicable to problems in both rectangular and polar coordinates. The convergence analysis at advanced time level is briefly discussed. The proposed methods are then compared with the corresponding successive over relaxation (SOR) and Newton-SOR iterative methods both in terms of accuracy and performance.
Citation: International Journal of Computer Mathematics (2009), 86(9): 1556-1571
Issue Date: 2009
Keywords: AGE method
Cubic spline method
Newton-AGE method
Quasi-linear parabolic equation
Singular equation
ISSN: 207160
Author Scopus IDs: 22938082300
Author Affiliations: Mohanty, R.K., Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India
Jain, M.K., Department of Mathematics, Indian Institute of Technology, New Delhi, India, 4076, C/4, Vasant Kunj, New Delhi-110 070, India
Corresponding Author: Mohanty, R. K.; Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India; email:
Appears in Collections:Journal Publications [HY]

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