In this chapter we discuss discrete variable methods for solving BVPs for ordinary differential equations. These methods produce solutions that are defined on a set of discrete points. Methods of this type are initial-value techniques, i.e., shooting and superposition, and finite difference schemes. We will discuss initialvalue and finite difference methods for linear and nonlinear BVPs, and th...

In the first part of this chapter we focus on the question of well-posedness of boundary-value problems for linear partial differential equations of elliptic type. The second part is devoted to the construction and the error analysis of finite difference schemes for these problems. It will be assumed throughout that the coefficients in the equation, the boundary data and the resulting solution ...

Abstract We study some functionals associated with a process driven by fractional boundary value problem (FBVP for short). By FBVP we mean Cauchy condition written in terms of equation, that is an equation involving time-fractional derivative the sense Caputo. focus on lifetimes and additive characterizing conditions. show corresponding are related to telegraph equations. Moreover, order gives ...

In this paper, we consider differential equations whose degeneracy is due to the presence of a matrix operator coefficient derivative perturbed by small parameter. Properties are applied analysis boundary layer in solutions initial-boundary-value problems for considered. Regularity conditions determined.