A SIMPLE METHOD OF SOLVING NONLINEAR INTEGRODIFFERENTIAL AND INTEGRODIFFERENCE EQUATIONS

A number of asymptotic methods [5, 6] have been developed in automatic control theory [1], phase locking [2, 3], and certain radiophysical p roblems [4] for solving nonlinear integrodifferential and integrodiffe rence equations. However, they involve laborious calculations, which i n some cases make it extremely difficult to find approximate solutions of sufficiently high order. Furthermore, the amount of calculation re quired increases considerably as the dimensions of the equations being solved increases. Finally, existing publications contain no general a symptotic methods for solving nonlinear difference equations. Only in [3, 4] and in some other papers [7, 8] are special methods given for s olving such equations. In the present paper, we shall generalize the m ultiscale method [9, 10], which is highly efficient and enables one to find fairly easily approximations of high order for a wide class of n onlinear integrodifferential and integrodifference equations, The meth od is illustrated with the problem of determining the pull-in range of a pulsed phase-locked loop system with a delay in the feedback circui t.