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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 821907, 13 pages
Research Article

-Stable Derivative-Free Error-Corrected Trapezoidal Rule for Burgers' Equation with Inconsistent Initial and Boundary Conditions

Department of Mathematics, BITS Pilani, Rajasthan, Pilani 333031, India

Received 25 March 2012; Revised 19 August 2012; Accepted 21 August 2012

Academic Editor: Theodore E. Simos

Copyright © 2012 Lajja Verma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We combine suitable arithmetic average approximations, with explicit backward Euler formula, and derive a third-order -stable derivative-free error-corrected trapezoidal rule (LSDFECT). Then, we apply LSDFECT rule to the linearized Burgers' equation with inconsistent initial and boundary conditions and test its stability and exactness. We use Mathematica 7.0 for computation.