Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Article type: Research Article
Authors: Mohanty, R.K.
Affiliations: Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi – 110 007, India
Abstract: In this piece of work, we discuss two new two-level implicit difference formulas of O(k2+h2)and O(k2+h4) in a coupled manner for the numerical solution of quasi-linear partial differential equation A(x,t,u,ux,uxx,uxxx)uxxxx+ut=f(x,t,u,ux,uxx,uxxx), 0 < x < 1, t > 0 subject to the initial condition u(x,0)=g0(x), 0≤x≤1 and boundary conditions u(0,t)=p0(t), ux(0,t)=q0(t), u(1,t)=p1(t), ux(1,t)=q1(t), t≥0, where k > 0 and h > 0 are grid spacing in t- and x-directions, respectively. In both cases, we use only three spatial grid points and do not require to discretize the boundary conditions. The numerical solution of ux is obtained as a by-product of the method. The stability analysis for a model problem is discussed. The methods are successfully applied to the problems in polar coordinates. Numerical examples are given to demonstrate the utility of new methods and their convergence.
Keywords: Unsteady biharmonic problem, Quasi-linear, Implicit scheme, Polar coordinates, Singular point, Non-linear KdV equation, RMS errors
DOI: 10.3233/JCM-2003-3201
Journal: Journal of Computational Methods in Sciences and Engineering, vol. 3, no. 2, pp. 193-208, 2003
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
USA
Tel: +1 703 830 6300
Fax: +1 703 830 2300
sales@iospress.com
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
IOS Press
Nieuwe Hemweg 6B
1013 BG Amsterdam
The Netherlands
Tel: +31 20 688 3355
Fax: +31 20 687 0091
info@iospress.nl
For editorial issues, permissions, book requests, submissions and proceedings, contact the Amsterdam office info@iospress.nl
Inspirees International (China Office)
Ciyunsi Beili 207(CapitaLand), Bld 1, 7-901
100025, Beijing
China
Free service line: 400 661 8717
Fax: +86 10 8446 7947
china@iospress.cn
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
如果您在出版方面需要帮助或有任何建, 件至: editorial@iospress.nl