In this paper, we discuss an extended form of generalized quasilinearization technique for first order nonlinear impulsive differential equations with a nonlinear three-point boundary condition. In fact, we obtain monotone sequences of upper and lower solutions converging uniformly and quadratically to the unique solution of the problem.

Fractional Galilei invariant advection–diffusion (GIADE) equation, along with its more general version that is the GIADE equation nonlinear source term, discretized by coupling weighted and shifted Grünwald difference approximation formulae Crank–Nicolson technique. The new of backward substitution method, a well-established class meshfree methods, proposed for numerical consequent equation. In...

Abstract In this paper, we develop an optimized hybrid block method which is combined with a modified cubic B-spline method, for solving non-linear partial differential equations. particular, it will be applied three well-known problems, namely, the Burgers equation, Buckmaster equation and FitzHugh–Nagumo equation. Most of developed methods in literature equations have not focused on optimizin...

In this paper, the boundary value inverse problem related to generalized Burgers–Fisher and Burgers–Huxley equations is solved numerically based on a spline approximation tool. B-splines with quasilinearization Tikhonov regularization methods are used obtain new numerical solutions problem. First, method linearize equation in specific time step. Then, linear combination of approximate largest o...

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...

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...

Advances in automatic control theory may be seen to have two main objectives the synthesis of improved controllers for a given plant and the extension of the range of plants considered for control. Optimal control theory and its application to linear stems is an example of the former, whilst advances in the latter have been largely concerned with describing-function and quasilinearization techn...