Solution method of the nonlinear equations of mathemathical physics by the influence function

The nonhomogeneous differencial equation was investigated by means of a method of the influence function for the problems of nonlinear beam dynamics in the solenoid magnetic field up to the third order. The algorithms within the matrix formalism to obtain the solution of nonlinear equations by the influence function method, are described. Formulas - a view of the influence function and the solution of the nonhomogeneous differencial equation are received for the potentials responsible for the nonhomogeneity in the investigated differential equation. The program is written for analytical and numerical solutions (results for the considered application are given).