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A numerical algorithm for the nonlinear Kirchhoff string equation
  • J. Peradze
  • Mathematics, Computer Science
    Numerische Mathematik
  • 1 December 2005
TLDR
The initial boundary value problem is considered for the dynamic string equation and the Galerkin method, the modified Crank-Nicolson difference scheme used to perform approximation with respect to spatial and time variables, and also a Picard type iteration process for solving the system of nonlinear equations obtained by discretization are considered.
A Numerical Algorithm for a Kirchhoff-Type Nonlinear Static Beam
  • J. Peradze
  • Mathematics, Computer Science
    J. Appl. Math.
  • 30 August 2009
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
The existence of a solution and a numerical method for the Timoshenko nonlinear wave system
The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time
An Approximate Algorithm for a Kirchhoff Wave Equation
  • J. Peradze
  • Mathematics, Computer Science
    SIAM J. Numer. Anal.
  • 1 April 2009
The initial boundary value problem for a hyperbolic-type quasilinear equation $w_{tt}=\varphi(\int_0^\pi w_x^2dx)w_{xx}$ is considered. Its solution is derived by means of a numerical algorithm
On the approximate solution of a Kirchhoff type static beam equation
Abstract The paper deals with a boundary value problem for the nonlinear integro-differential equation u ⁗ − m ( ∫ 0 l u ′ 2 d x ) u ″ = f ( x , u ) , m ( z ) ≥ α > 0 , 0 ≤ z ∞ , modelling the static
A Kirchhoff type equation in a nonlinear model of shell vibration
The paper deals with the study of the initial boundary value problem for the Donnell-Mushtari-Vlasov nonlinear system of differential equations, which describes large deflections of a rectangular
Iterative Solution of a Nonlinear Static Beam Equation
We consider a boundary-value problem for the nonlinear integrodifferential equation u ′ ′ ′ ′ − m ∫ 0 l u ′ 2 dx u ″ = f x u u ′ , m z ≥ α > 0 , 0 ≤ z < ∞ , $$ {u}^{\prime \prime \prime \prime
A Galerkin–Newton Algorithm for Solution of a Kirchhoff-Type Static Equation
In this paper, an algorithm is proposed to find an approximate solution for the Kirchhoff -type nonlinear differential equation, which describes the static state of a beam. The solution of the
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