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A Numerical Method For Solving Fuzzy Initial Value Problems, Safa Emad Al-Refai
A Numerical Method For Solving Fuzzy Initial Value Problems, Safa Emad Al-Refai
Theses
In this thesis, the optimized one-step methods based on the hybrid block method (HBM) are derived for solving first and second-order fuzzy initial value problems. The off-step points are chosen to minimize the local truncation error of the proposed methods. Several theoretical properties of the proposed methods, such as stability, convergence, and consistency are investigated. Moreover, the regions of absolute stability of the proposed methods are plotted. Numerical results indicate that the proposed methods have order three and they are stable and convergent. In addition, several numerical examples are presented to show the efficiency and accuracy of the proposed methods. …
On Vector Sequence Transforms And Acceleration Techniques, Steven L. Hodge
On Vector Sequence Transforms And Acceleration Techniques, Steven L. Hodge
Mathematics & Statistics Theses & Dissertations
This dissertation is devoted to the acceleration of convergence of vector sequences. This means to produce a replacement sequence from the original sequence with higher rate of convergence.
It is assumed that the sequence is generated from a linear matrix iteration xi+ i = Gxi + k where G is an n x n square matrix and xI+1 , xi,and k are n x 1 vectors. Acceleration of convergence is obtained when we are able to resolve approximations to low dimension invariant subspaces of G which contain large components of the error. When …