A new iterative integral formulation for semilinear equations based on the generalized quasilinearization theory

This paper presents a new iterative integral approach for solving semilinear equations. The integral formulation is derived based on the generalized quasilinearization theory in which nonlinear equations are replaced by a set of iterative linear equations. An advantage of the new formulation is that its convergence is guaranteed under a given condition and the convergence rate can be quadratic. The effectiveness of the new approach has been demonstrated on several examples of the nonlinear Poisson type. Comparisons with some existing methods and a study of the convergence rate have also been conducted in this work.