| Summary: | algebra, general topology, and functional analysis. The fourth chapter titled “Research Methodology” is possibly the most important part of this dessirtation. In this chapter the research features; are ix �discussed (section A) together with instruments utilization (section B), the research elements (section C) and the construction of NHPODE algorithm (section D). Chapter five shows the results obtained from the execution of NHPODE algorithm for solving various types of nonlinear systems (section A). Section B contains the discussion concerning the results, which are shown in the previous section. A cornparsion betwwen NHPODE and other algorithms as QuasiNewton, Brent and Brown are included in section C. An application of hornotopy methods to solve problems in the electrical engineering is explained i n chapter five also. Finally, chapter six consists of three sections. Section A contains the conclusion of the research. Section B shows the complexity concerning the research while section C consists of many suggegtions and open problems. This work contains three appendix, these are appendix A, which contains the list of M ATLAB program, section B which explains the output of the algorithm program and appendix C which consists of figures concerning the paths obtained from solving nonlinear systems by using the NHPODE algorithm.
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