He covers basic equations of continuous media, the basics of the theory of finite-difference schemes, methods for solving systems of algebraic equations, methods for solving boundary value problems for systems of equations, wave propagation problems, finite-difference splitting methods for solving dynamic problems, solving elastoplastic dynamic and quasi-static problems with finite deformations, and modeling damage and fracture in inelastic materials and structures.

1 Introduction We consider the following nonlinear second-order Dirichlet boundary value problem y'' + f(x, y, y') = 0, x [member of] [a, b] (1.

In practice, SODEs are frequently treated as either initial value problems (IVPs) or boundary value problems (BVPs).

Keywords: Difference equation, nonlocal, boundary value problem.

After this, there is a large number of works in which the method has been developed for different boundary value problems, thus first, second and higher order ordinary differential equations with different type of boundary conditions as, among others, the periodic, mixed, Dirichlet or Neumann conditions, and partial differential equations of first and second order, have been treated in the literature.

Abstract In this paper, we consider the existence of multiple positive solutions for the following 2n-th order m-point boundary value problems: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [[alpha]].

Abstract We study the stability of positive solution to the boundary value problem [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.

s)] reproduce the boundary values assumed in their derivation ([partial derivative][u.