Additive schemes (splitting schemes) for some systems of evolutionary equations
For computational scientists solving coupled PDE systems, this work provides a method to handle time-derivative coupling, but the contribution is incremental as it extends existing splitting techniques.
The paper develops additive (splitting) schemes for systems of evolutionary PDEs where time derivatives are coupled, extending previous work that only considered spatial coupling. The proposed triangular two-component splitting yields efficient numerical algorithms for initial-boundary value problems.
On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied problems the individual components of the vector of unknowns are coupled together and then splitting schemes are applied in order to get a simple problem for evaluating components at a new time level. Typically, the additive operator-difference schemes for systems of evolutionary equations are constructed for operators coupled in space. In this paper we investigate more general problems where coupling of derivatives in time for components of the solution vector takes place. Splitting schemes are developed using an additive representation for both the primary operator of the problem and the operator at the time derivative. Splitting schemes are based on a triangular two-component representation of the operators.