scholarly journals Solution of a Schrödinger equation by iterative refinement

1990 ◽  
Vol 32 (1) ◽  
pp. 115-131 ◽  
Author(s):  
Rekha P. Kulkarni ◽  
Balmohan V. Limaye
Keyword(s):  
Fixed Point ◽  
Galerkin Method ◽  
Error Bounds ◽  
Initial Approximation ◽  
Simple Eigenvalue ◽  
Numerical Results ◽  
Iterative Refinement ◽  
Point Scheme ◽  
The Galerkin Method ◽  
Better Than

AbstractA simple eigenvalue and a corresponding wavefunction of a Schrödinger operator is initially approximated by the Galerkin method and by the iterated Galerkin method of Sloan. The initial approximation is iteratively refined by employing three schemes: the Rayleigh-Schrödinger scheme, the fixed point scheme and a modification of the fixed point scheme. Under suitable conditions, convergence of these schemes is established by considering error bounds. Numerical results indicate that the modified fixed point scheme along with Sloan's method performs better than the others.

scholarly journals On error bounds in strong approximations for eigenvalue problems

1981 ◽  
Vol 22 (3) ◽  
pp. 270-283 ◽  
Author(s):  
R. P. Kulkarani ◽  
B. V. Limaye
Keyword(s):  
Numerical Experiment ◽  
Galerkin Method ◽  
Error Bounds ◽  
Strong Approximation ◽  
Eigenvalue Problems ◽  
Strong Approximations ◽  
Asymptotic Case ◽  
The Galerkin Method

AbstractSome corrections of error bounds obtained by Chatelin and Lemordant for the first three terms of the asymptotic case of a strong approximation are given. The error bounds for the approximations of order 2 in the Galerkin method are compared with the Rayleigh quotients constructed with the eigenvectors in the Sloan method. A numerical experiment is also carried out.

Mode Localization in a Grouped Bladed Disk

2000 ◽  
Author(s):  
J. H. Kuang ◽  
B. W. Huang
Keyword(s):  
Galerkin Method ◽  
Rotation Speed ◽  
Numerical Results ◽  
Mode Localization ◽  
Crack Distribution ◽  
Bladed Disk ◽  
Localization Phenomenon ◽  
Blade Assembly ◽  
The Galerkin Method ◽  
Blade Crack

The effect of local blade crack on the mode localization in a rotating turbo disk with a group-blade assembly was studied. Periodically coupled Euler-Bernoulli beams were used to approximate the grouped and shrouded turbo blades. The cracked blade, regardedas a local disorder, was modeled using a two-span beam. A spring was imposed on this two-span beam to characterize the local crack. The Galerkin method was applied to formulate the localization equations of the mistuned system. Numerical results indicate that the blade crack, crack distribution and rotation speed in a rotating group-blades disk may affect the localization phenomenon significantly.

scholarly journals Existence of Solutions of a Nonlocal Elliptic System via Galerkin Method

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Alberto Cabada ◽  
Francisco Julio S. A. Corrêa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Galerkin Method ◽  
Positive Solution ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions ◽  
Dimensional System ◽  
The Galerkin Method

By means of the Galerkin method and by using a suitable version of the Brouwer fixed-point theorem, we establish the existence of at least one positive solution of a nonlocal ellipticN-dimensional system coupled with Dirichlet boundary conditions.

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 On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

Sign in / Sign up

Export Citation Format

Share Document