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Intermediate boundary conditions for time-split methods applied to hyperbolic partial differential equations. (English) Zbl 0596.65062
The paper considers time-split methods for systems \(u_ t=A(x,t,u)u_ x\), with A an r-dimensional matrix with real eigenvalues. In these methods the matrix A is split into a sum \(A_ f+A_ s\) and then a step \(t\to t+\Delta t\) for the integration of \(u_ t=Au_ x\) consists of one or several steps of a numerical scheme consistent with \(v_ t=A_ fv_ x\), interspersed with one or several steps of a numerical scheme consistent with \(w_ t=A_ sw_ x\). In several space dimensions, the usefulness of the splitting idea is well known; the advantages in one- dimensional settings were discussed by the present author and J. Oliger [ibid. 40, 469-497 (1983; Zbl 0516.65075)]. The paper suggests a technique for the derivation of accurate and stable boundary conditions for the intermediate nonphysical solutions v and w. Numerical experiments are also reported.
Reviewer: J.M.Sanz-Serna

MSC:
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
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