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Numerical solutions of nonlinear elliptic problem using combined-block iterative methods

UNCW Author/Contributor (non-UNCW co-authors, if there are any, appear on document)
Fang Liu (Creator)
The University of North Carolina Wilmington (UNCW )
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Abstract: This thesis is concerned with iterative and monotone methods for numerical solutions of nonlinear elliptic boundary value problems. The methods we study here are called block iterative methods, which solve the nonlinear elliptic problems in twodimensional domain in R2 or higher dimensional domain in Rn. In these methods the nonlinear boundary value problem is discretized by the finite difference method. Two iteration processes, block Jacobi and block Gauss-Seidel monotone iterations, are investigated for computation of solutions of finite difference system using either an upper solution or a lower solution as the initial iteration. The numerical examples are presented for both linear and nonlinear problems, and for both block and pointwise methods. The numerical results are compared and discussed.

Additional Information

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
Boundary value problems, Differential equations, Elliptic, Differential equations, Elliptic--Numerical solutions, Iterative methods (Mathematics), Nonlinear theories
Boundary value problems
Iterative methods (Mathematics)
Nonlinear theories
Differential equations, Elliptic
Differential equations, Elliptic -- Numerical solutions