عنوان	Collocation Technique Approach for Approximation Solution of Integral and Integro-Differential Equations Using Orthogonal Polynomials
نوع پژوهش	پایان نامه
کلیدواژه‌ها	Integral and integro-differential equations, Standard collocation method, Orthogonal polynomials, Basis functions, Approximate solution, Gaussian elimination method.
چکیده	In this thesis, an approximate method based on the collocation technique utilizing orthogonal polynomials is presented for the numerical solution of linear integral and integro-differential equations. The unknown function is expanded as a linear combination of orthogonal polynomials, and by selecting optimal collocation nodes (the roots of shifted Chebyshev polynomials), the original problem is transformed into a system of linear algebraic equations. A rigorous convergence analysis is provided using operator theory and Banach space frameworks, demonstrating that the method?s error diminishes at a rate of $\mathcal{O}(h^q)$, where $q$ denotes the polynomial degree and $h$ represents the mesh size. For validation and performance assessment, numerical results obtained from the proposed method are compared with those of the hat functions method. Computational experiments on benchmark examples confirm that the orthogonal polynomial-based approach not only achieves higher accuracy and faster convergence but also offers simpler implementation and reduced sensitivity to node distribution compared to the hat functions method.
پژوهشگران	روشنک لطفی کار (استاد راهنما)، احمد قاسم عاشور (دانشجو)