A reduced finite difference scheme based on singular value decomposition and proper orthogonal decomposition for Burgers equation
By using reduced basis techniques for solving partial differential equation, the computational cost can be decreased both in terms of memory and time. In this article the authors consider the Burgers' equation. By singular value decomposition of the matrix where the columns are snapshots of the solution to the equation, the reduced basis is taken as the set of singular vectors corresponding to the singular values larger than some prescribed constant. In the numerical experiments the snapshots are taken from the finite difference solution of the corresponding equation. The author also proves some error bounds for the solution obtained with the developed reduced basis technique.
scientific article; zbMATH DE number 5564248
scientific article