Iterative methods particularly the Two-Parameter Alternating Group Explicit (TAGE) methods are used to solve system of linear equations generated from the discretization of two-point fuzzy boundaryvalueproblems (FBV...
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Iterative methods particularly the Two-Parameter Alternating Group Explicit (TAGE) methods are used to solve system of linear equations generated from the discretization of two-point fuzzy boundaryvalueproblems (FBVPs). The formulation and implementation of the TAGE method are also presented. Then numerical experiments are carried out onto two example problems to verify the effectiveness of the method. The results show that TAGE method is superior compared to GS method in the aspect of number of iterations, execution time, and Hausdorff distance.
We study boundaryvalueproblems for q-difference equations and inclusions with nonlocal and integral boundary conditions which have different quantum numbers. Some new existence and uniqueness results are obtained by...
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We study boundaryvalueproblems for q-difference equations and inclusions with nonlocal and integral boundary conditions which have different quantum numbers. Some new existence and uniqueness results are obtained by using fixed point theorems. Examples are given to illustrate the results.
In this paper, using fixed point index and the mixed monotone technique, we present some multiplicity and uniqueness results for the singular nonlocal boundaryvalueproblems involving nonlinear integral conditions. O...
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In this paper, using fixed point index and the mixed monotone technique, we present some multiplicity and uniqueness results for the singular nonlocal boundaryvalueproblems involving nonlinear integral conditions. Our nonlinearity may be singular in its dependent variable and it is allowed to change sign.
By using an infinitely many critical points theorem, we study the existence of infinitely many solutions for a fourth-order nonlinear boundaryvalue problem, depending on two real parameters. No symmetric condition on...
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By using an infinitely many critical points theorem, we study the existence of infinitely many solutions for a fourth-order nonlinear boundaryvalue problem, depending on two real parameters. No symmetric condition on the nonlinear term is assumed. Some recent results are improved and extended.
We study functional-differential equations with unbounded variable operator coefficients and variable delays in a Hilbert space. We prove the well-posed solvability of initial-boundaryvalueproblems for the above-men...
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We study functional-differential equations with unbounded variable operator coefficients and variable delays in a Hilbert space. We prove the well-posed solvability of initial-boundaryvalueproblems for the above-mentioned equations in Sobolev spaces of vector functions on the positive half-line.
We consider a boundaryvalue problem for a fourth-order equation on a graph modeling elastic deformations of a plane rod system with conditions of rigid connection at the vertices. Conditions for the unique solvabilit...
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We consider a boundaryvalue problem for a fourth-order equation on a graph modeling elastic deformations of a plane rod system with conditions of rigid connection at the vertices. Conditions for the unique solvability are stated. We also present sufficient conditions for the problem to be degenerate.
For a fractional ordinary differential equation with the Dzhrbashyan-Nersesyan operator, we prove a theorem on the existence and uniqueness of a solution of a boundaryvalue problem with shift.
For a fractional ordinary differential equation with the Dzhrbashyan-Nersesyan operator, we prove a theorem on the existence and uniqueness of a solution of a boundaryvalue problem with shift.
We construct and justify the asymptotics of the solution of a boundaryvalue problem for a singularly perturbed system of two second-order ordinary differential equations that contain distinct powers of a small parame...
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We construct and justify the asymptotics of the solution of a boundaryvalue problem for a singularly perturbed system of two second-order ordinary differential equations that contain distinct powers of a small parameter multiplying second-order derivatives for the case of a multiple root of the degenerate equation. The root multiplicity results in changes in the structure of the asymptotics of the boundary layer solution as compared with the case of a simple root, in particular, in changes in the scale of the boundary layer variables.
We study an iteration method for a first-order differential-operator equation with a nonlinear operator in a separable Hilbert space. The convergence of the iterative process is proved in the strong norms. Convergence...
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We study an iteration method for a first-order differential-operator equation with a nonlinear operator in a separable Hilbert space. The convergence of the iterative process is proved in the strong norms. Convergence estimates are derived. We present an application of the suggested method to the solution of a model initial-boundaryvalue problem for a fourth-order parabolic equation.
In our earlier paper we argued that for the decomposition (1) to be valid, the operator V, which we denoted as Helec, must be written as a direct integral over clamped-nuclei electronic Hamiltonians, the integral bein...
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In our earlier paper we argued that for the decomposition (1) to be valid, the operator V, which we denoted as Helec, must be written as a direct integral over clamped-nuclei electronic Hamiltonians, the integral being taken over all nuclear positions; we further suggested that after this correction an expansion analogous to (5) would be problematic. The operator Helec has purely continuous spectrum extending from some minimum value to on the real-axis; it has no true eigenvalues, and no normalizable eigenvectors in the Hilbert space L2(x, X). We emphasize that this description is entirely in agreement with the mathematical physics literature but not with the conventional Born-Huang discussion summarized above, since the distinction between Ho (Xf ) and its direct integral Helec is obvious and fundamental. The recent work of Jecko7 gives a critical mathematical summary of the Born-Oppenheimer approximation including the expansion approach described by (3).(7), and emphasizes the fundamental role of spectral projection for operators with continuous spectra. Thus, it is very much to the point that there is no complete set of eigenfunctions in Hilbert space for the clamped-nuclei Hamiltonian Ho(Xf ) required for the expansion (5) (and likewise for Helec). This is crucial since the Born-Huang method effectively writes the clamped nuclei Hamiltonian in a spectral form using the geigenfunctions to provide a resolution of the identity [ABSTRACT FROM AUTHOR]
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