NEWTONIAN ITERATIVE SCHEME WITH SIMULTANEOUS ITERATIONS OF INVERSE DERIVATIVE

A modification of the Continuous Analogy of Newton Method for the nume rical solving of nonlinear problems is suggested. Ir permits one to re place the inversion of the derivative operator on every step of iterat ions by its inversion only in the initial approximation point, Then th e extended system of the differential equations in Hilbert space, intr oduced in the work, permits the realization of the iterative process w ith the simultaneous calculation of the inverse derivative operator. T he convergence theorem is proved for the method under almost the same conditions as for CANM. Numerical calculations for the model problem ( Kirchhoff equation) have shown the effectiveness and adequately fast c onvergence of the iterative schemes based on the suggested method.