Keywords: additive splitting scheme, iterative splitting scheme, heat transfer, Crank-Nicolson scheme, porous media.

In this paper, we construct and compare algorithms based on additive and iterative splitting schemes for solving systems of partial differential equations. While the additive schemes reduce the computational time as a result of the simplification of only needing to invert the diagonal part of the operator matrix, the iterative schemes use an acceleration of analytically solvable exponential operator matrices. From the theoretical point of view, iterative splitting methods are alternating Picard fixed point iteration schemes, while additive splitting schemes are additive operator difference schemes. For practical applications, it is important to obtain fast splitting schemes and simply calculable algorithms with highly accurate results.

In this paper we concentrate on developing such algorithms and compare the additive and iterative splitting schemes with regard to fully coupled semi-discretised differential equations.

In the first part, we formulate the additive and iterative splitting schemes and study their orders of convergence. In the second part, we propose different test examples, which compare the standard splitting schemes with the proposed additive and iterative schemes. Finally, we present a real-life problem of heat tranfer.

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