L-Stable Block Backward Differentiation Formula for Parabolic Partial Differential Equations
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In this paper, an L-stable Second Derivative Block Backward Differentiation Formula (SDBBDF) of order 5 is presented for the solutions of parabolic equations. It applied the use of the classical method of lines for the discretization of the parabolic equations. The method reduces the one-dimensional parabolic partial differential equation which has integral or non-integral boundary conditions to a system of Ordinary Differential Equations (ODEs) with initial conditions. The stability properties of the block method are investigated using the boundary locus plot and the method was found to be L-stable. The derived method is implemented on standard problems of parabolic equations and the results obtained show that the method is accurate and efficient.
Parabolic equation , Method of lines , L-stability , Second Derivative Block Backward Differentiation Formula , Research Subject Categories::MATHEMATICS
Akinnukawe, B. I., Akinfenwa, O. A., & Okunuga, S. A. (2016). L-Stable Block Backward Differentiation Formula for Parabolic Partial Differential Equations. Ain Shams Engineering Journal, 7(2), 867-872.