要約

A new method for finding an approximate solution of the Cauchy problem for systems of linear ordinary differential equations is proposed. The approximate solution is represented as a linear combination of the elements of a system of linearly independent functions. The unknown constants of expansion into a series are found from the condition of the best approximation of the right-hand sides of the differential equations of the system (by the norm L₂ [0, 1]) and their derivatives (by the norm W₂ [0, 1]), using the indicated system of linearly independent functions. Examples are given.