Symbolic Solving of Differential Equations with Partial Derivatives

An algorithm for the symbolic solving of systems of linear partial differential equations by means of multivariate Laplace-Carson transform (LC) is produced. Considered is a system of K linear equations with M as the greatest order of partial derivatives and right hand parts of a special type, that permits a symbolic Laplace-Carson transform. Initial conditions are input. As a result of Laplace-Carson transform of the system according to the initial conditions, we obtain an algebraic system of equations. There exist efficient methods to solve large size systems of such types. It gives a possibility to implement the method for solving the large PDE systems. A method to obtain compatibility conditions is discussed. The application of LC allows one to execute it in a symbolic way.

systems of partial differential equations, Laplace-Carson transform, symbolic solving