Wavelet-Galerkin method for the Kolmogorov equation
It is well understood that wavelet functions, especially Daubechies' wavelets [cf. \textit{I. Daubechies}, Commun. Pure Appl. Math. 41, 909--996 (1988; Zbl 0644.42026)] provide a powerful tool that can be applied in the finite element method. Using Daubechies' wavelets as basis functions, the authors solve here Kolmogorov equation by a wavelet-Galerkin method. The process consists in deriving a method called the time dependent boundary wavelet Galerkin method. With this method, an initial interval, for the initial-boundary value problem based upon the initial condition of the Kolmogorov equation is determined. Based upon the numerical solution of the initial-boundary value problem, this interval is adjusted during computation. An example is also provided by using Daubechies D4 scaling functions.
scientific article; zbMATH DE number 2167465
scientific article