Dissertation > Excellent graduate degree dissertation topics show

A Numerical Method for Solving Schrodinger Equation Basing on the Meshless Method

Author: WangGuoDong
Tutor: JiangTongSong
School: Qufu Normal University
Course: Operational Research and Cybernetics
Keywords: Schr(O ¨)dinger equation Finite difference Radial basis functions Numerical solution
CLC: O241
Type: Master's thesis
Year: 2011
Downloads: 34
Quote: 0
Read: Download Dissertation

Abstract


During the last two decades, meshless methods have been developed and ef-fectively applied to solve many problems in science and engineering. The meshless methods do not need the grid very much, and it can avoid the grid distorted and twisted problem. It can give expression to particular advantages in some areas, which the finite element method and the boundary method could not solve.The schrodinger equation is an important partial differential equation,it is applied in various fields. In the current work we investigate a different approach to find the solution of the schrodinger equation. This paper presents a numerical scheme to solve the two-dimensional (2D) time-dependent schrodinger equation using the method of particular solutions.We generalize some meshless methods in this article, using the different functions is the major difference in different meshless methods.The layout of the paper is as follows:The first chapter is an introduction. We describe the application back-grounds and the research situations of the meshless methods.In the second chapter, we propose an important meshless method, which is called radial basis function. The radial basis functions play an important part in developing of meshless methods, and it solves a lot of partial differential equation problems.In the third chapter, We describe the application backgrounds and the re-search situations of the method of fundamental solutions. And we give the char-acteristics of this method.In the fourth and fifth chapters, we propose the method of particular so-lutions and some of application of this method. In the fifth chapter, based on the finite difference scheme and radial basis functions, we give a new numerical scheme using one of the meshless method which is called the method of partic-ular solutions for solving two-dimensional time-dependent schrodinger equation. Two numerical examples with good accuracy are given to validate the proposed method.

Related Dissertations

  1. American Option Pricing under Stochastic Market Option Model Based on Dividend and Treatment Fees,O211.6
  2. Dynamic Simulation and Experimental Research of Towed Low-tension Cable Based on Generalized α Method,U661
  3. Research the Model and Development the Software of Secondary Cooling for Beam Blank Continuous Casting,TF777
  4. Inverse Problems of Determining Multi-Point Sources Based on Diffusion Models,O3
  5. The Hole Repairing in Surface Based on Partial Differential Equations,O186.11
  6. Numerical of Non-Fourier Heat Conduction and Thermal Stress,O343.6
  7. Numerical Method for Some Kinds of Partial Differential Equations about Solitary Wave,O241.82
  8. The Study of Several Force Gradient Symplectic Algorithms,O241
  9. The Numerical Solution of a Class of Singular Perturbation Problems,O241.8
  10. A Finite Element Method for Schr(?)dinger Equation with Neumann Boundary Conditions in an Unbounded Strip,O241.82
  11. Structure Excavation Numerical Simulation and Distortion Forecast Research,TU470.3
  12. Integrable Discretizations to a Class of Soliton Equations,O175.2
  13. The Research on Characteristics of Optical-control Two-wavelength Terahertz Modulator Based on Photonic Crystal,TN761
  14. Finite Difference Aanalysis on Fast Response of Liquid Crystal Device Base on OCB Mode,TN873.93
  15. Study on Metal-dielectric Subwavelength Waveguide Structure,TN929.1
  16. The Study on Characterisce of Multi-wavegength Phtonic Crsytal Wavelength Division Multiplexers Based Multimode Interference Thoery,TN929.11
  17. A Study of GPU-based FDTD Method and Its Application in LED Performance Optimization,TN312.8
  18. The Research of Chafee-Infante Reaction Diffusion Equations Solving Problems,O175.2
  19. Surface Plasmon Resonance and Optical Properties of Photonic Crystals,O53
  20. The Study on Graded Photonic Crystals Resonant Cavity in the Terahertz Region,O734
  21. Numerical Simulate for a Class of MHD Equations Problem’s Blow-up Criterion,O351.2

CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis
© 2012 www.DissertationTopic.Net  Mobile