Justification of a numerical-analytic method of successive approximations for problems with integral boundary conditions

TL;DR: In this paper, the existence of solutions of integro-differential equations with integral boundary conditions with deviating arguments was investigated by establishing a comparison result and applying the monotone iterative technique.

TL;DR: In this article, a uniform finite difference method on a Bakhvalov mesh was proposed to solve a quasilinear first order parameterized singularly perturbed problem with integral boundary conditions.

TL;DR: In this article, the application of the numerical-analytic method proposed by A.M. Samoilenko in 1965 to multipoint boundary value problems is analyzed, and the results show that the numerical analysis can be used to solve the problem.

TL;DR: In this paper, the numerical analytic method is applied to systems of differential equations with parameter under the assumption that the corresponding functions satisfy the Lipschitz conditions in matrix notation, and several existence results for problems with deviations of an argument are obtained.

TL;DR: The theory of approximate methods for solving mathematical problems has been studied extensively in the literature, see as discussed by the authors for a survey of some of the most important results in functional analysis. But the authors' aim has not been to give an exhaustive account, even of the principal known results.

TL;DR: In this paper, a method to improve convergence of successive approximations in the study of existence and in the constructin of approximate solutions of nonlinear differential equations in the case of periodic and linear two-point boundary conditions is presented.

TL;DR: In this paper, the authors studied the number of linearly independent solutions of the equationy(n) (x)+(Fy)(x)+ρn��y (x)=0,x∃ [0, 1], in which F is a bounded linear operator acting on various normed function spaces.