Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations

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

“…A similar set of linear equations but with a better convergence can be constructed based on the generalized quasilinearization theory proposed by Bellman and Kalaba [12] and later further developed by Lakshmikantham and Koksal [13]. It reads…”

“…In this paper a different iterative scheme is employed and a corresponding integral formulation is derived with the aim of achieving a fast convergence rate without the need of increasing the size of the discretized system. This scheme is based on the generalized quasilinearization theory [12,13]. Under certain circumferences, a quadratic convergence rate is guaranteed even when the nonlinearity is severe.…”

Generalized monotone iterative technique for set differential equations involving causal operators with memory

“…To get a comprehensive view on this technique refer [7,10]. There has been continuous development in this area and some of the papers recently published in this area involving various problems are given in the references [5,6,13].…”

Numerical investigation of generalized quasilinearization method for reaction diffusion systems

“…This method has been extended, generalized and refined so that it includes the situation when the forcing function is the sum of a convex and concave function. See [1,[8][9][10] for details. This result has been referred to as the generalized quasilinearization (GQL) method.…”