Dissertation > Excellent graduate degree dissertation topics show

Unconditional Dissipative Difference Scheme for the Cahn-hilliard Equation

Author: QinHaiXia
Tutor: HeLiPing
School: Shanghai Jiaotong University
Course: Computational Mathematics
Keywords: Five-point difference scheme Periodic boundary Semi-implicit predictor-corrector method The nine o'clock differential method Cahn-Hilliard equation with variable coefficients
CLC: O241.82
Type: Master's thesis
Year: 2010
Downloads: 40
Quote: 0
Read: Download Dissertation

Abstract


In this paper , we mainly examine two-dimensional Cahn-Hilliard equation periodic boundary problem and proposed a series of fully discrete dissipative finite difference scheme . Semi-implicit predictor-corrector method further , focusing on narrative the five-point difference format is used for the Cahn-Hilliard Equation solving constant coefficient and Cahn-Hilliard equation with variable coefficients in the second half of this paper , the existence and uniqueness of the numerical solution of the Cahn-Hilliard equation to explore with a five-point difference and nine differential method numerical simulation to show the effectiveness of the formats mentioned . Finally, we discuss the Cahn-Hilliard equation with variable coefficients , and gives the corresponding numerical results and listed in the table , we can draw many conclusions about the time step the first chapter describes the background and current status of the Cahn-Hilliard equation . the second chapter estimated difference method . proposed a five-point difference scheme Cahn-Hilliard equation . , consider the region Ω = [0 , L ] × [ 0 , periodic boundary L] in this chapter , we describe some notations on the numerical solution (1.1) , and then establish some important lemmas Chapter to prove the existence of the numerical solution of the format ( 2.8) given and uniqueness. lemma and corollary . fourth chapter is some proof about the convergence of the numerical solution . fifth chapter introduces some numerical results in this chapter , we explore the Cahn-Hilliard equation nine difference scheme for the Cahn-Hilliard equation with variable coefficients , we are given a specific differential format .

Related Dissertations

  1. Studies on Finite Difference Method of Option Pricing Equation,F830.9
  2. Existence of Positive Solutions of Periodic Boundary Value Problem with a Parameter,O175.8
  3. Three-dimensional target random rough underlying surface electromagnetic scattering of the FDTD method,TN011
  4. The Periodic Solutions and Periodic Boundary Value Problems for Functional Differential Equations,O175.8
  5. Existence and Multiplicity of Positive Solutions for Periodic Boundary Value Problems,O175
  6. Variational Iteration Method for Solving Periodic Boundary Value Problems,O241.8
  7. Numerical Simulation for Ratcheting of Particle Reinforced Metal Matrix Composites Based on Periodical Boundary Condition,TB331
  8. Time Periodic Solutions of Nonlinear Wave Equation,O175.29
  9. The Study of Vortex Dynamics Based on Time-Dependent Ginzburg-Landau Model for Superconductors,O511
  10. Multi-Scale Analyses of Damage Evolution in Woven Composite Materials,TB332
  11. Studies on the Attractor Bifurcation of Nonlinear Partial Differential Equations,O175.29
  12. Global Structure of Positive Solutions for Some Periodic Boundary Value Problems of Second-order Ordinary Differential Equations,O175.8
  13. LNG cold energy utilization process of enhanced heat transfer technology and gas-liquid two-phase flow in horizontal pipe Excitation Mechanism,TK124
  14. Nonlinear differential equations and its application,O175.8
  15. The Research of Transport Equations with General Boundary Conditions in Slab Geometry,O177.2
  16. Existence and Multiplicity of Solutions to High-order Differential Equation Periodic Boundary Value Problems,O175.8
  17. The Theory and Application of Solution about Abstract Equations,O175.6
  18. Periodic Solutions and Periodic Boundary Value Problems of Functional Differential Systems,O175
  19. Multiplicity of Positive Solutions to Singular Superlinear Second-order Periodic Boundary Value Problems,O175
  20. Boundary Value study of dynamic equations on time scales,O175.8

CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
© 2012 www.DissertationTopic.Net  Mobile