Locally linearized fractional step methods for nonlinear parabolic problems |
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Authors: | A Arrarás L Portero |
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Institution: | Dpto. de Ingeniería Matemática e Informática, Universidad Pública de Navarra Edificio de Las Encinas, Campus de Arrosadía, 31006-Pamplona, Spain |
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Abstract: | This work deals with the efficient numerical solution of a class of nonlinear time-dependent reaction-diffusion equations. Via the method of lines approach, we first perform the spatial discretization of the original problem by applying a mimetic finite difference scheme. The system of ordinary differential equations arising from that process is then integrated in time with a linearly implicit fractional step method. For that purpose, we locally decompose the discrete nonlinear diffusion operator using suitable Taylor expansions and a domain decomposition splitting technique. The totally discrete scheme considers implicit time integrations for the linear terms while explicitly handling the nonlinear ones. As a result, the original problem is reduced to the solution of several linear systems per time step which can be trivially decomposed into a set of uncoupled parallelizable linear subsystems. The convergence of the proposed methods is illustrated by numerical experiments. |
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Keywords: | 65M06 65M20 65M55 65Y05 |
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