Numerical solutions of nonlinear parabolic problems using combined-block iterative methods

UNCW Author/Contributor (non-UNCW co-authors, if there are any, appear on document)
Yaxi Zhao (Creator)
Institution
The University of North Carolina Wilmington (UNCW )
Web Site: http://library.uncw.edu/

Abstract: This paper is concerned with the block monotone iterative schemes of numerical solutions of nonlinear parabolic systems with initial and boundary condition in two dimensional space. By using the finite difference method, the system is discretized into algebraic systems of equations, which can be represented as block matrices. Two iterative schemes, called the block Jacobi scheme and the block Gauss-Seidel scheme, are introduced to solve the system block by block. The Thomas algorithm is used to solve tridiagonal matrices system efficiently. For each scheme, two convergent sequences starting from the initial upper and lower solutions are constructed. Under a sufficient condition the monotonicity of the sequences, the existence and the uniqueness of solution are proven. To demonstrate how these method work, the numerical results of several examples with different types of nonlinear functions and different types of boundary conditions are also presented.

Additional Information

Publication
Thesis
A Thesis Submitted to the University of North Carolina Wilmington in Partial Fulfillment of the Requirements for the Degree of Master of Science
Language: English
Date: 2009
Keywords
Algorithms, Differential equations Nonlinear, Differential equations Parabolic, Iterative methods (Mathematics), Nonlinear systems
Subjects
Nonlinear systems
Algorithms
Iterative methods (Mathematics)
Differential equations, Nonlinear
Differential equations, Parabolic