In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

Abstract We present two theoretical results and surprising conjectures concerning convergence properties of Broyden’s method for smooth nonlinear systems equations. First, we show that when is applied to a mapping $$F:\mathbb {R}^n\rightarrow \mathbb {R}^n$$ F : R <...

In this paper, we define the space Sαθ (∆mv, f) of all f)-lacunary statistical convergent sequences order α with help unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ mv and real number ∈ (0, 1]. We also introduce ωαθ strong summable α. Properties related to these spaces are studied. Inclusion relations between ωα θ established under certain conditions.

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI =...