Solutions For Multi-point Boundary Value Problems Research Articles

Application of a Modification of the Numerical-Analytic Method to the Multipoint Boundary-Value Problem for Volterra-Type Integrodifferential Equations

We substantiate the possibility of application of a modification of the numerical-analytic method of successive approximations to the solution of multipoint boundary-value problems for Volterra-type integrodifferential equations.

Limit Theorems for the Solutions of Multipoint Boundary-Value Problems with Parameter in Sobolev Spaces

We consider the most general class of multipoint boundary-value problems for systems of linear ordinary differential equations of any order whose solutions belong to a given Sobolev space $$ {W}_p^{n+r} $$ , with n ≥ 0, r ≥ 1, and 1 ≤ p ≤ ∞. We establish constructive sufficient conditions under which the solutions of the analyzed problems are continuous with respect to the parameter e for e = 0 in the space $$ {W}_p^{n+r} $$ .

Limit Theorems for the Solutions of Multipoint Boundary-Value Problems in Sobolev Spaces

We consider the most general class of multipoint boundary-value problems for systems of linear ordinary differential equations of the first order whose solutions belong to a given Sobolev space $$ {W}_p^n $$n ϵ ℕ, 1 ≤ p ≤ ∞: Sufficient constructive conditions under which the solutions of these problems are continuous with respect to the parameter e for e = 0 in the space $$ {W}_p^n $$ are established.

On the Construction of Asymptotics of the Solution of Multipoint Boundary-Value Problem for a Linear Degenerate Singularly Perturbed System of Differential Equations

We study the possibility of construction of the asymptotic solution of multipoint boundary-value problem for a linear singularly perturbed system of differential equations with identically degenerate matrix of derivatives in the case of multiple spectrum of the main operator. To this end, we use the results of asymptotic analysis for the general solution of a linear degenerate singularly perturbed system of differential equations. We establish the existence and uniqueness conditions for the solution of the analyzed boundary-value problem.

Triple symmetric positive solutions for multipoint boundary-value problem with one-dimensional [formula omitted]-Laplacian

In this paper, we consider the multipoint boundary value problem for one-dimensional p -Laplacian ( ϕ p ( u ′ ( t ) ) ) ′ + q ( t ) f ( t , u ( t ) , u ′ ( t ) ) = 0 , t ∈ ( 0 , 1 ) , subject to the boundary conditions: u ( 0 ) − ∑ i = 1 n μ i u ′ ( ξ i ) = 0 , u ( 1 ) + ∑ i = 1 n μ i u ′ ( η i ) = 0 , where ϕ p ( s ) = | s | p − 2 s , p > 1 , μ i > 0 , 0 < ξ 1 < ξ 2 < ⋯ < ξ n < 1 / 2 , ξ i + η i = 1 , i = 1 , 2 , … , n . Applying the fixed point theorem due to Avery and Peterson, we study the existence of at least three symmetric positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f contains the first-order derivative explicitly and the boundary condition is of Sturm–Liouville type.

Multipoint Boundary Conditions for Differential Operators

We establish differential properties of generalized solutions of multipoint boundary-value problems for ordinary differential equations.

Numerical solution of multipoint boundary-value problems in improved shell theory

For some classes of stratified shells subject to transverse shear (shells of revolution with parameters varying along the generatrix, noncircular cylindrical shells with characteristics varying along the directrix, rectangular shallow shells), we propose an approach that reduces the solution of multipoint boundary-value problems to a number of two-point problems. As an example, we consider the stressed state of an open noncircular cylindrical shell supported in some section along the generatrix.

An approach to numerical solution of multipoint boundary-value problems

An approach is proposed to solving multipoint boundary-value problems for linear differential equation of w-th order, based on reduction to two-point boundary-value problems. The two-point problems are solved by the stable discrete orthogonalization method. Some numerical examples are considered.

The solution of systems of equations using the 𝜖-algorithm, and an application to boundary-value problems

In this paper, the authors describe the properties of an algorithm to solve systems of nonlinear equations. The algorithm does not use any derivatives. The convergence of this algorithm is quadratic under quite mild conditions. This method can also be used to solve systems of linear equations with infinitely many solutions. The second part of the paper is devoted to the application of this algorithm to the solution of multipoint boundary-value problems for differential equations. A theorem of convergence is proved and various numerical examples are given.

Solution of state-constrained optimal control problems through quasilinearization

Quasilinearization is extended to the numerical solution of multi-point boundary-value problems for ordinary differential equations. It is described how such problems arise from state-constrained optimal control problems. A simple numerical example is given to illustrate the method.

Quasilinearization, system identification and prediction

This paper is devoted to a mathematical formulation and computational solution of the problems of system identification and the determination of unmeasurable state variables on the basis of observations of a process, two topics of central importance in the design of adaptive controllers. The approach suggested—based on the theory of quasilinearization—is an outgrowth of continuing RAND research on the computational solution of multi-point boundary-value problems.