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We found solvability conditions and a construction of the generalized Green operator for a linear matrix boundary-value problem; we present an operator that reduces a linear matrix equation to the conventional linear Noether boundary-value problem. To solve a linear matrix system, we use the operator that reduces a linear matrix equation to a linear algebraic equation with a rectangular matrix.
Green function for boundary value problems in heat conduction equation
Spacecraft guidance - boundary value problem
Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.
Numerical solution for variety of nonlinear degenerate elliptic boundary value problems, and convergence of associated iterative procedures
Numerical methods for mixed boundary value problem of axisymmetric shells of revolution, using truncated series expansion and finite difference expressions
Modified quasilinearization method for solving nonlinear, two point boundary value problems
Solution of ferrite boundary value problem in rectangular waveguide and resolution of Lewin paradox
Discrete ordinate method for boundary value problems in gas dynamics using differential equations yields solutions to Couette flow
A self-consistent version of the compressible boundary-value problem for configurations with leading-edge vortex separation is formulated, based on the assumption that the compressible flow field is controlled by the linearized potential equation. The stream surface boundary condition and the zero pressure jump condition of the compressible free vortex flows are analyzed; application of the Goethert rule permits the compressible nonlinear boundary-value problem for the subsonic flow domain to be transformed into an equivalent nonlinear incompressible problem. The compressibility corrections developed are used in numerical calculations of subsonic leading-edge vortex flows about planar wing geometries. The sample calculations, employing an inviscid flow model in which the wing and vortex sheets are represented by piecewise continuous quadratic doublet sheet distributions, are applicable to high subsonic Mach numbers.
The results of Goldberg and Tadmor (1985) are extended to achieve improved stability criteria for a large class of approximations to the initial boundary value problem associated with a particular hyperbolic system in a quarter plane. In a stability analysis, it is shown that the entire approximation is stable if and only if the scalar outflow components of its principal part are stable. Thus, the global stability question is reduced to that of a scalar, homogeneous outflow problem. The stability criteria for the reduced problem, which depend both on the basic scheme and the boundary conditions, but very little on the interaction between the two, are stated and used to establish previous examples and new ones, including a host of dissipative and nondissipative examples. There is no difficulty in extending the stability criteria to two-boundary problems and initial-boundary value problems with variable coefficients.
Finite-volume applications of high-order accurate ENO schemes to two-dimensional boundary-value problems are studied. These schemes achieve high-order spatial accuracy, in smooth regions, by a piecewise polynomial approximation of the solution from cell averages. In addition, this spatial operation involves an adaptive stencil algorithm in order to avoid the oscillatory behavior that is associated with interpolation across steep gradients. High-order TVD Runge-Kutta methods are employed for time integration, thus making these schemes best suited for unsteady problems. Fifth- and sixth-order accurate applications are validated through a grid refinement study involving the solutions of scalar hyperbolic equations. A previously proposed extension for the Euler equations of gas dynamics is tested, including its application to solutions of boundary-value problems involving solid walls and curvilinear coordinates.
We consider the class of boundary value problems for elliptic, parabolic, and hyperbolic equations in cylinders separated by a two-layer film into two half-cylinders. We prove the existence and uniqueness theorem and express the solutions in terms of solutions to analogous classical problems in cylinders without films.
Round-off errors in difference solutions of boundary value problems for elliptic equations and systems
Nonlinear two-point boundary-value problem solution by combined techniques of quasilinearization and method of particular solutions
Infinite dimensional multipoint methods and solution of two point boundary value problems
Finite difference solution to mixed boundary value problem for Laplace equation
We consider the structure of branching of the solution of a nonlinear boundary-value problem of the theory of shells in the case of cylindrical shell with delamination area subjected to the action of external pressure. To find the solution, we use the generalized Kantorovich method applied to the analysis of the corresponding boundary-value problem. The complete structure of branching is presented for the solutions of the problem. We establish the existence of branches of the solution both with forms of deformation and joint deformation of the layers and with forms of deformation and separate deformation of the layers in the delamination region.