Numerical solution of some partial differential equations by means of a deterministic method of approximate functional integration

A numerical method of solution of some partial differential equations is presented. The method is based on representation of Green functions of the equations in the form of functional integrals and subsequent approximate calculation of the integrals with the help of a deterministic approach. In this case the solution of the equations is reduced to evaluation of usual (Riemann) integrals of relatively low multiplicity. A procedure allowing one to increase accuracy of the solutions is suggested. The features of the method are investigated on examples of numerical solution of the Schrödinger equation and related diffusion equation.