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Table of Contents:
Chapter 1: Introduction
– Background of the Study
– Statement of the Problem
– Purpose of the Study
– Research Questions
– Significance of the Study
– Organization of the Thesis

Chapter 2: Literature Review
– Overview of Numerical Analysis
– Finite Element Methods
– Finite Difference Methods
– Comparison of Methods
– Previous Studies on Numerical Analysis
– Gaps in Existing Literature

Chapter 3: Research Methodology
– Research Design
– Data Collection Methods
– Data Analysis Techniques
– Sampling Strategy
– Ethical Considerations
– Research Limitations

Chapter 4: Discussion of Findings
– Analysis of Results
– Interpretation of Data
– Comparison with Previous Studies
– Implications for Practice
– Recommendations for Future Research

Chapter 5: Conclusion and Summary
– Summary of Findings
– Conclusion
– Contributions to the Field
– Limitations of the Study
– Recommendations for Practitioners
– Suggestions for Future Research

Brief Overview on Numerical Analysis: Finite Element Methods and Finite Difference Methods:
Numerical Analysis is a field of study that focuses on the development and implementation of algorithms to solve mathematical problems using numerical methods. In this thesis, the focus is on Finite Element Methods and Finite Difference Methods, two commonly used numerical techniques for solving partial differential equations.

Finite Element Methods involve dividing a domain into smaller elements and approximating the solution within each element using basis functions. This method is widely used in engineering and physics for solving problems with complex geometries.

Finite Difference Methods, on the other hand, discretize the domain into a grid and approximate the derivatives of the solution using the difference equations. This method is often used in finance, heat transfer, and fluid dynamics.

The literature review will provide an overview of these methods, compare their strengths and weaknesses, and identify gaps in existing research. The research methodology will outline the design of the study, data collection methods, and analysis techniques. The discussion of findings will analyze the results, interpret the data, and provide recommendations for practitioners.

Overall, this thesis aims to contribute to the field of Numerical Analysis by comparing Finite Element Methods and Finite Difference Methods and identifying areas for future research and improvement.

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