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M. T. Ashordia 《Differential Equations》2010,46(2):167-181
For a linear Kurzweil generalized differential system with singularities, we consider two-point boundary value problems of two forms. The singularity is understood in the sense that the matrix and vector functions defining the system may have infinite total variation. 相似文献
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The method of parallel shooting for the solution of two-point boundary value problems is investigated. Bounds are obtained for the norms of the fundamental matrices of the differential equations and their inverses. These bounds are used for estimation of the condition number and for determining the shooting intervals.This research was supported by NASA Grant No. NGR-002-016.Visiting Utah State University, Summer, 1971. 相似文献
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This paper presents variational and bivariational bounds associated with the linear equation Aφ = f, with general mixed boundary conditions. The variational results bound the action f, φ> + boundary terms, while the bivariational results bound g, φ>, where g is an arbitrary function. 相似文献
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A new direction in the theory of general linear boundary value problems is explored. The starting point is an explicit Volterra factorization of the Green's matrix (and related kernels) associated with the problem. This result leads to (1) imbedding of the boundary value problems, (2) initial value algorithms for their solution, and (3) comparison theorems relating two different boundary value problems with a common boundary condition. Extensions and connections with earlier work in this area are presented. 相似文献
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A new formalism in the theory of linear boundary value problems involving causal functional differential equations is presented. The approach depends on the construction of a differentiable family of boundary problems into which the original boundary value problem is imbedded. The formalism then generates an initial value problem which is equivalent to the family of imbedded problems. An important aspect of the method is that the equations in the initial value algorithm are ordinary differential equations rather than functional differential equations, although nonlinear and of higher dimension. Applications of the theory to differential-delay and difference equations are given. 相似文献
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Jesús Rodríguez Kristen Kobylus Abernathy 《Journal of Mathematical Analysis and Applications》2012,385(1):49-59
Our goal in this paper is to provide sufficient conditions for the existence of solutions to discrete, nonlinear systems subject to multipoint boundary conditions. The criteria we present depends on the size of the nonlinearity and the set of solutions to the corresponding linear, homogeneous boundary value problems. Our analysis is based on the Lyapunov–Schmidt Procedure and Brouwer?s Fixed Point Theorem. The results presented extend the previous work of D. Etheridge and J. Rodríguez (1996, 1998) [5], [6] and J. Rodríguez and P. Taylor (2007) [18], [19]. 相似文献
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Summary. We present symmetric collocation methods for linear differential-algebraic boundary value problems without restrictions on
the index or the structure of the differential-algebraic equation. In particular, we do not require a separation into differential
and algebraic solution components. Instead, we use the splitting into differential and algebraic equations (which arises naturally
by index reduction techniques) and apply Gau?-type (for the differential part) and Lobatto-type (for the algebraic part) collocation
schemes to obtain a symmetric method which guarantees consistent approximations at the mesh points. Under standard assumptions,
we show solvability and stability of the discrete problem and determine its order of convergence. Moreover, we show superconvergence
when using the combination of Gau? and Lobatto schemes and discuss the application of interpolation to reduce the number of
function evaluations. Finally, we present some numerical comparisons to show the reliability and efficiency of the new methods.
Received September 22, 2000 / Revised version received February 7, 2001 / Published online August 17, 2001 相似文献