Basics of Ultra-Fast Numerical Solution of Some Differential Equations of Mathematical Physics

The majority of simulation in various fields like radio engineering, electronics, etc.) are based on PDE, in particular, the Laplace, Poisson equations, the wave equation, the equation of thermal conductivity, etc., which are the basis for the development of mathematical models. It is known that the efficiency of used mathematical models is determined by the speed and adequacy of numerical solutions of these equations. An approach that does not require solving the systems of equations and allows a parallel implementation of the numerical solution, which eventually leads to faster calculations in comparison with the known methods, is proposed.