Cathrine Tegnander

Splitting errors using generalized symmetries: Applications to convection/reaction/diffusion equations.

DIFTA 2004–04–30

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Abstract: We study local splitting errors of partial differential equations (PDEs) on the form

u_t = A(u, ∇_X u, ∇_X²u, …) + B(u, ∇_Xu, ∇_X²_u, &hellip),

where X∈ R^m, u∈ R^q, and A and B are operators.

The errors are estimated by Lie analysis and generalized symmetries. We study splittings of the exact problems as well as corresponding semi-discretized equations.

The formal errors are illustrated by examples from convection/diffusion/reaction equations.