Adjointness properties for differential systems with eigenvalue‐dependent boundary conditions, with application to flow‐duct acoustics

1977 ◽  
Vol 61 (4) ◽  
pp. 913-922 ◽  
Author(s):  
Robert E. Kraft ◽  
William R. Wells
Keyword(s):  
Boundary Conditions ◽  
Differential Systems ◽  
Duct Acoustics ◽  
Eigenvalue Dependent Boundary Conditions ◽  
Flow Duct

LYAPUNOV-TYPE INEQUALITIES FOR LOCAL FRACTIONAL DIFFERENTIAL SYSTEMS

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050131
Author(s):  
YONGFANG QI ◽  
LIANGSONG LI ◽  
XUHUAN WANG
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Analytical Method ◽  
Systematic Design ◽  
Differential Systems ◽  
Design Algorithm ◽  
Fractional Differential Systems ◽  
Lyapunov Inequalities ◽  
Fractional Differential

This paper deals with the problem of Lyapunov inequalities for local fractional differential equations with boundary conditions. By using analytical method, a novel Lyapunov-type inequalities for the local fractional differential equations is provided. A systematic design algorithm is developed for the construction of Lyapunov inequalities.

Sturm–Liouville problems with non-separated eigenvalue dependent boundary conditions

2000 ◽  
Vol 130 (2) ◽  
pp. 239-247 ◽  
Author(s):  
P. A. Binding ◽  
P. J. Browne
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Separated Boundary Conditions ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions

Sturm–Liouville differential equations are studied under non-separated boundary conditions whose coefficients are first degree polynomials in the eigenparameter. Situations are examined where there are at most finitely many non-real eigenvalues and also where there are only finitely many real ones.

scholarly journals EVALUATION OF SEVERAL NONREFLECTING COMPUTATIONAL BOUNDARY CONDITIONS FOR DUCT ACOUSTICS

1995 ◽  
Vol 03 (04) ◽  
pp. 327-342 ◽  
Author(s):  
WILLIE R. WATSON ◽  
WILLIAM E. ZORUMSKI ◽  
STEVE L. HODGE
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Sound Propagation ◽  
Sparse Matrix ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Substantial Reduction ◽  
Sound Attenuation ◽  
Interior Solution ◽  
Duct Acoustics

Several nonreflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each nonreflecting boundary condition. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate than the local ones considered. Results also show that this condition is more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other nonreflecting conditions.

Boundary value problems for systems of second order differential equations

1985 ◽  
Vol 101 (1-2) ◽  
pp. 61-76 ◽  
Author(s):  
L. H. Erbe ◽  
H. W. Knobloch
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Existence Of A Solution ◽  
Differential Systems ◽  
Second Order Differential Equations

SynopsisWe consider boundary value problems for second order differential systems of the form (1)x” = A(t)x′ + f(t, x) and (2) x” = A(t)x′ + f(t, x) + q(t, x). By assuming the existence of a solution to (1) with a given region in (t, x) space, we derive conditions under which there exists a solution to (2) which stays in a certain neighbourhood of and satisfies given boundary conditions.

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