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From structured data to evolution linear partial differential equations
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DOI：10.1016/j.jcp.2019.04.049.png)
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Abstract
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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 [6], 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. Crown Copyright (C) 2019 Published by Elsevier Inc. All rights reserved.
Keywords:
Partial differential equations
Numerical approximation
Operator symbols
Pseudospectral methods
Inverse problems
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