From structured data to evolution linear partial differential equations
Journal of Computational Physics , Volume 393 p. 162- 185
This paper is devoted to the derivation of computational methods for constructing partial differential equations from data. Following some recent works [7,14,15,20], we propose a methodology based on symbolic calculus [8,9,13], pseudospectral methods [2,3] and stochastic processes , in order to determine non-constant coefficients of linear evolution Partial Differential Equations (PDEs), from a set of structured data constituted by solutions at given times and positions, of an unknown linear PDE.
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Lorin, E. (2019). From structured data to evolution linear partial differential equations. Journal of Computational Physics, 393, 162–185. doi:10.1016/j.jcp.2019.04.049