Dissertation > Excellent graduate degree dissertation topics show

High Order Finite Difference Methods for Several Partial Differential Equations

Author: ChenYouZuo
Tutor: ZhangLuMing
School: Nanjing University of Aeronautics and Astronautics
Course: Computational Mathematics
Keywords: Burgers equation Cole-Hopf transformation Compact Difference Scheme Burgers-Fisher equation Three - layer difference scheme Two-dimensional heat conduction equation Nonlocal boundary conditions Kronecker product
CLC: O241.82
Type: Master's thesis
Year: 2009
Downloads: 46
Quote: 0
Read: Download Dissertation

Abstract


In this paper, some partial differential equations high order accuracy difference scheme . The first part of the one-dimensional Burgers equation with initial boundary value problem based on the Cole-Hopf transformation Compact Difference Scheme and theoretical results show that the format has a fourth-order numerical accuracy and unconditional stability . Verified by numerical experiments to calculate the effect of the difference scheme and the convergence order . The second part of the initial value problem of the Burgers-Fisher equation construct three explicit difference scheme with second-order accuracy , the format has higher accuracy than the existing non-standard differential format and more relaxed stability conditions, can be calculated to take a larger time step length , thereby saving computation time . Numerical experiments show that the format has good stability and efficiency of this article . The third part of the two-dimensional heat conduction equation with Neumann boundary condition nonlocal boundary question the a tight alternating direction differential format , and use of the the matrix Kronecker tensor product of nature proved the the unique solvability format and unconditional stability , numerical test to verify the order of convergence of the difference scheme .

Related Dissertations

  1. The Research on Nonsingular Solution of the Sylvester Equation Based on Quadratic System Decoupling,O175
  2. A Class of Fractional Orthogonal Transforms and Their Applications,TN911.7
  3. Research and Implementation based the gray theory algebra encryption algorithm,TP393.08
  4. The Lattice Boltzmann Method for Some Nonlinear Partial Differential Equations,O241.82
  5. Compact Difference Scheme for Elliptic Equations with Variable Coefficients,O241.82
  6. The Problem of Partitioning of Graphs into Connected Subgraphs and the Connectivity of Kronecker Product of Graphs,O157.5
  7. Some Topological Indices and Vulnerability Parameters of Kronecker Products of Graphs,O157.5
  8. The Discontinuous Galerkin Finite Element Method for Burgers Equation,O241.82
  9. A class of second-order variable coefficient nonlinear partial differential equations B ( ? ) Cklund transformation classification,O175.29
  10. Local Artificial Boundary Conditions for One-dimensional Burgers’ Equation,O241.82
  11. Research on Petrov-Galerkin Spectral Method for Two Problems,O241.82
  12. Painleve analysis and exact solutions of the Boussinesq-Burgers equation,O175.29
  13. Large Time Asymptotics for the Generalized BBM-Gurgers Equation,O175.8
  14. The Research of Numerical Method for the KdV Equation with Space-time Perturbations,O241.82
  15. Three difference scheme for a class of nonlinear coupled Burgers equation,O175
  16. Numerical Methods Analysis on Two Kinds of Delay Differential Equations,O241.82
  17. Helmholtz equation and algorithm Compact Difference Scheme,O241.82
  18. The product of the two types of automatic machines study,TP301.1
  19. Weakly damped generalized KdV equation and generalized KdV-Burgers equation of state for a long time,O175.2
  20. The Finite Volume Element Method for Two-Dimensional Burgers Equation,O241.82

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