Numerical algorithm for the third-order partial differential equation with local boundary conditions

2017 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Kheireddine Belakroum ◽  
Assia Guezane-Lakoud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential ◽  
Local Boundary ◽  
The Third

scholarly journals Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type

2001 ◽  
Vol 26 (7) ◽  
pp. 417-426 ◽  
Author(s):  
M. Denche ◽  
A. L. Marhoune
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Mixed Problem ◽  
Mixed Type ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential ◽  
Integral Boundary ◽  
Equation Of Mixed Type

We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem.

scholarly journals A note on the nonlocal boundary value problem for a third order partial differential equation

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 801-808 ◽  
Author(s):  
Kh. Belakroum ◽  
A. Ashyralyev ◽  
A. Guezane-Lakoud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Order Partial Differential Equation ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space with a self-adjoint positive definite operator is considered. Applying operator approach, the theorem on stability for solution of this nonlocal boundary value problem is established. In applications, the stability estimates for the solution of three nonlocal boundary value problems for third order partial differential equations are obtained.

Nonlinear Vibrations of Non-Uniform Beams Including Inertia Effects

2005 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Ion Stroe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Nonlinear Partial Differential Equation ◽  
Nonlinear Effects ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Inertia Effects

This papers deals with nonlinear vibrations of non-uniform beams with geometrical nonlinearities such as moderately large curvatures, and inertia nonlinearities such as longitudinal and rotary inertia forces. The nonlinear fourth-order partial-differential equation describing the above nonlinear effects is presented. Using the method of multiple scales, each effect is found by reducing the nonlinear partial-differential equation of motion to two simpler linear partial-differential equations, homogeneous and nonhomogeneous. These equations along with given boundary conditions are analytically solved obtaining so-called zero-and first-order approximations of the beam’s nonlinear frequencies. Since the effect of mid-plane stretching is ignored, any boundary conditions could be considered as long as the supports are not fixed a constant distance apart. Analytical expressions showing the influence of these three nonlinearities on beam’s frequencies are presented up to some constant coefficients. These coefficients depend on the geometry of the beam. This paper can be used to study these influences on frequencies of different classes of beams. However, numerical results are presented for uniform beams. These results show that as beam slenderness increases the effect of these nonlinearities decreases. Also, they show that the most important nonlinear effect is due to moderately large curvature for slender beams.

scholarly journals I. On curvature and orthogonal surfaces

1873 ◽  
Vol 21 (139-147) ◽  
pp. 166-167
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Orthogonal System ◽  
The Other ◽  
Third Order ◽  
Partial Differential ◽  
The Third ◽  
The Subject

The principal object of the present Memoir is the establishment of the partial differential equation of the third order satisfied by the parameter of a family of surfaces belonging to a triple orthogonal system. It was first remarked by Bouquet that a given family of surfaces does not in general belong to an orthogonal system, but that (in order to its doing so) a condition must be satisfied: it was afterwards shown by Serret that the condition is that the parameter considered as a function of the coordinates must satisfy a partial differential equation of the third older, this equation was not obtained by him or the other French geometers engaged on the subject, although methods of obtaining it, essentially equivalent but differing in form, were given by Darboux and Levy.

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