From structured data to evolution linear partial differential equations
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.
|Keywords||Inverse problems, Numerical approximation, Operator symbols, Partial differential equations, Pseudospectral methods|
|Journal||Journal of Computational Physics|
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