Boundary value problems initial condition identification by a wavelet-based Galerkin method.

In this study, we introduce a numerical method to reconstruct, from posterior measurements of the solution, the initial condition in the one-dimensional heat conduction problem. The method uses a wavelet-based Galerkin method for the spatial discretization and spectral decomposition of the basis stiffness matrix to get the numerical solution without time discretization as in classical approaches. In fact, according to the proposed method, setting an error bound and properly selecting the eigenvalues of the discretization system, we are able to reconstruct the initial conditions without exceeding the required error. The applicability and computational efficiency of the methods are investigated by solving some numerical examples with toy solutions and the experimental results confirm its accuracy. [ABSTRACT FROM AUTHOR]