scholarly journals A Numerical Algorithm for a Kirchhoff-Type Nonlinear Static Beam

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Jemal Peradze
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problem ◽  
Galerkin Method ◽  
Numerical Algorithm ◽  
Boundary Value ◽  
Iteration Process ◽  
Beam Equation ◽  
Nonlinear Static ◽  
The Galerkin Method ◽  
Nonlinear Iteration

A boundary value problem is posed for an integro-differential beam equation. An approximate solution is found using the Galerkin method and the Jacobi nonlinear iteration process. A theorem on the algorithm error is proved.

scholarly journals A new method for high-order boundary value problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yingchao Zhang ◽  
Liangcai Mei ◽  
Yingzhen Lin
Keyword(s):  
Approximate Solution ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Numerical Algorithm ◽  
Time Complexity ◽  
Numerical Experiments ◽  
Orthonormal Basis ◽  
Boundary Value ◽  
High Order

AbstractThis paper presents a numerical algorithm for solving high-order BVPs. We introduce the construction method of multiscale orthonormal basis in $W^{m}_{2}[0,1]$ W 2 m [ 0 , 1 ] . Based on the orthonormal basis, the numerical solution of the boundary value problem is obtained by finding the ε-approximate solution. In addition, the convergence order, stability, and time complexity of the method are discussed theoretically. At last, several numerical experiments show the feasibility of the proposed method.

Non-Newtonian oscillatory layer flow, approximate solution

1979 ◽  
Vol 44 (10) ◽  
pp. 2908-2914 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Galerkin Method ◽  
Horizontal Plane ◽  
Oscillatory Flow ◽  
Oscillatory Boundary Layer ◽  
Layer Flow ◽  
Pseudoplastic Liquid ◽  
The Galerkin Method

The problem of the oscillatory flow of pseudoplastic liquid in vicinity of the infinitely long horizontal plane is formulated in stresses. For Re i.e. for conditions of oscillatory boundary layer the problem is solved approximately by the Galerkin method.

scholarly journals Application of Initial Boundary Value Problem on Logarithmic Wave Equation in Dynamics

2018 ◽  
Author(s):  
Shkelqim Hajrulla ◽  
Leonard Bezati ◽  
Fatmir Hoxha
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Boundary Value Problem ◽  
Sobolev Inequality ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Logarithmic Sobolev Inequality ◽  
Initial Boundary Value ◽  
The Galerkin Method

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

Analysis of the Relaxation of Wall Electrons in a Plasma

1975 ◽  
Vol 30 (8) ◽  
pp. 937-946
Author(s):  
G. Ecker ◽  
K.-U. Riemann ◽  
A. Scholz
Keyword(s):  
Integral Equation ◽  
Kinetic Equation ◽  
Singular Integral Equation ◽  
Boundary Value Problem ◽  
Singular Integral ◽  
Boundary Value ◽  
Iteration Process ◽  
Standard Technique ◽  
Inelastic Collisions ◽  
Zeroth Order

Abstract A procedure is developed which renders the simultaneous description of angular and energy relaxation of wall electrons in a plasma possible. The plasma is assumed to be field free, allowance is made for elastic and inelastic collisions with neutrals, as well as for electron-electron encounters. The procedure is based on an expansion in terms of the eigenfunctions of a suitable part of the kinetic equation. In the zeroth order, the problem is reduced to a boundary value problem of the Sturm type, and subsequent solution of a singular integral equation by standard technique. To account for the rest of the kinetic equation, we construct a Green′s function which forms the basis for an iteration process. The application of the procedure is illustrated with an example.

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