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Home  >  Volume 21 (2012)

Lax convergence principle of a linear multi-step scheme for solving parabolic equation by Odio Augustine Onyejuwa, Volume 21 (July, 2012), pp 315 - 318
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A linear multi-step scheme is considered for the solution of a parabolic equation. The function u, takes values in suitable subspaces of the space of definition of the system under study. Such a function u is said to be admissible and so, it therefore admit the Taylor series expansion. A practical result for convergence was obtained on the application of the equivalent theorem of Lax. Based on this theorem, we establish that the scheme is consistent and stable which implied that the scheme converge.  

Keywords: consistency, stability, convergence difference equation, linear multi-step scheme, equivalent theorem of Lax and wave equation.