A quasilinearization approach for parameter identification in nonlinear abstract Cauchy problems

Quasilinearization Approach to Nonlinear Problems in Physics

The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method could be proved are formulated and elaborated. The method, whose mathematical basis in physics was discussed recently by one of the present authors (VBM), approximates the solution of a nonlinear differential equation by treating the nonlinear terms as a perturbation about the li...

Inhomogeneous Two-Parameter Abstract Cauchy Problem

Haar Wavelet Quasilinearization Approach for Solving Nonlinear Boundary Value Problems

Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y. More accurate solutions are obtained by wavelet decomposition in the form of a multiresolution analysis of the function which represents solution of boundary value problems. Through this ana...

inhomogeneous two-parameter abstract cauchy problem

Parameter Identification for Nonlinear Ill-posed Problems

Since the classical iterative methods for solving nonlinear ill-posed problems are locally convergent, this paper constructs a robust and widely convergent method for identifying parameter based on homotopy algorithm, and investigates this method’s convergence in the light of Lyapunov theory. Furthermore, we consider 1-D elliptic type equation to testify that the homotopy regularization can ide...