NOTE: Monotone Iterative Technique for a Nonlinear Integral Equation

Monotone Iterative Technique for Semilinear Elliptic Systems

We develop monotone iterative technique for a system of semilinear elliptic boundary value problems when the forcing function is the sum of Caratheodory functions which are nondecreasing and nonincreasing, respectively. The splitting of the forcing function leads to four different types of coupled weak upper and lower solutions. In this paper, relative to two of these coupled upper and lower so...

Latus: A new accelerator for generating combined iterative methods in solving nonlinear equation

Monotone Iterative Technique for Integral Boundary Value Problems of Singular Differential Equations on the Whole Line

This paper deals with the existence of positive solutions for some boundary value problems of the singular differential equations on the whole line. Our approach is based on the fixed point theorem and the monotone iterative technique. Without the assumption of the existence of lower and upper solutions, we obtain not only the existence of nonnegative solutions for the problems, but also establ...

Iterative Regularization Methods for Ill-Posed Hammerstein Type Operator Equation with Monotone Nonlinear Part

We considered a procedure for solving an ill-posed Hammerstein type operator equation KF (x) = y, by solving the linear equation Kz = y first for z and then solving the nonlinear equation F (x) = z. Convergence analysis is carried out by means of suitably constructed majorizing sequences. The derived error estimate using an adaptive method proposed by Perverzev and Schock (2005) in relation to ...

A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions

In this paper, an effective technique is proposed to determine thenumerical solution of nonlinear Volterra-Fredholm integralequations (VFIEs) which is based on interpolation by the hybrid ofradial basis functions (RBFs) including both inverse multiquadrics(IMQs), hyperbolic secant (Sechs) and strictly positive definitefunctions. Zeros of the shifted Legendre polynomial are used asthe collocatio...