Cubature of Multidimensional Schr?dinger Potential Based on Approximate Approximations

摘要

We report here on some recent results obtained in collaboration with Maz'ya and Schmidt (Appl Anal 98:408-429, 2019). We derive semi-analytic cubature formulas for the solution of the Cauchy problem for the Schrodinger equation which are fast and accurate also if the space dimension is greater than or equal to 3. We follow ideas of the method of approximate approximations, which provides high-order semi-analytic cubature formulas for many important integral operators of mathematical physics. The proposed method is very efficient in high dimensions if the data allow separated representations.