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.
Numerical solutions of nonlinear parabolic problems using combined-block iterative methods
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Created on 1/1/2009
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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