The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order differential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.

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.

This article concentrates on the effect of MHD heat mass transfer on the stagnation point nanofluid flow over a stretching or shrinking sheet with homogeneous-heterogeneous reactions. The flow analysis is disclosed in the neighborhood of stagnation point. Features of heat transport are characterized with Newtonian heating. The homogeneous-heterogeneous chemical reaction between the fluid and di...

A stair Laguerre pseudospectral method is proposed for numerical solutions of differential equations on the half line. Some approximation results are established. A stair Laguerre pseudospcetral scheme is constructed for a model problem. The convergence is proved. The numerical results show that this new method provides much more accurate numerical results than the standard Laguerre spectral me...

in this paper, the chebyshev spectral collocation method(cscm) for one-dimensional linear hyperbolic telegraph equation is presented. chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. a straightforward implementation of these methods involves the use of spectral differentiation matrices. firstly, we transform ...

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...