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Nonintrusive model order reduction for cross-diffusion systems. (English) Zbl 1501.65089

The authors present a nonintrusive ROM model for cross-diffusion equations, which is used to predict lots of patterns. Firstly, they present the matrix form discretized by the finite difference method, then show the algorithm. Finally, several numerical rests are given to show the efficiency of this algorithm. However, they only give some artificial examples, in my opinion, they should choose examples from the real life, then do the simulation and compare it with other methods.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
65D12 Numerical radial basis function approximation
65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A69 Multilinear algebra, tensor calculus
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35K51 Initial-boundary value problems for second-order parabolic systems
35K58 Semilinear parabolic equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
92D25 Population dynamics (general)
92C40 Biochemistry, molecular biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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References:

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