Numerical Methods : Lecture 06 Fixed Point Method (Existence, Uniqueness, Convergance, Estimation)

In this video, we focused to the Fixed Point Method, a foundational topic in Numerical Methods. We begin by exploring the existence and uniqueness of fixed points, using mathematical concepts of Fixed Point Theorem. Then, we discuss the conditions for convergence of the iterative method and how to ensure the method leads to accurate solutions. Finally, we address error estimation, providing tools to measure the maximum iterations for required accuracy. Whether you're a student aiming to master numerical methods or an engineer applying these techniques in real-world problems, this video offers a clear and comprehensive explanation of the Fixed Point Method with step-by-step examples. 🔢 Topics Covered: * Introduction to Fixed Point Iteration * Existence and Uniqueness of Fixed Points * Convergence Criteria * Error Analysis and Estimation 📚 Perfect for students of Numerical Methods, Engineering, Mathematics, and anyone interested in computational problem-solving. Linkedin Account : https://www.linkedin.com/in/muhammad-nouman-aslam-khan-60057722/?lipi=urn%3Ali%3Apage%3Ad_flagship3_feed%3BkSWSu7iJSPW3IHgRawrAAQ%3D%3D #numericalmethods #approximate #bisectionmethod #newtonraphsonmethod #chemicalengineering #materialsengineering #engineering #overview #numericalanalysis #MATLAB #NumericalDifferentiation #taylorseries #error #roundoff #absolute #intermediate#value#theorem #bisectionmethod #pseudocode #fixed #fpm #iterations #fixedpointtheorem #convergence #uniqueness #existence #bounds #numericalanalysislecture #errorapproximation #engineeringmathematics #appliednumericalmethodsforengineers #numericalmethods4thsemester