Weighted Residual Methods Focus on Collocation Method | Finite Element Analysis | SNS Institutions
Автор: Arun kumar R
Загружено: 2026-02-20
Просмотров: 2
Описание: #snsinstitutions #snsdesignthinkers #designthinking In this video, we introduce Weighted Residual Methods with a clear focus on the Collocation Method, a simple yet powerful technique for obtaining approximate solutions to differential equations when exact analytical solutions are not available. The idea behind weighted residual methods is to assume an approximate trial function with unknown coefficients, substitute it into the governing differential equation, and define a residual that represents how far the approximation deviates from the true solution. In the Collocation Method, the residual is forced to be zero at selected points in the domain, called collocation points, which leads to a system of algebraic equations for the unknown coefficients. This approach is intuitive, easy to implement, and computationally efficient, making it popular in numerical analysis and engineering applications. The video walks through the full procedure step by step, including the choice of trial functions, selection of collocation points, formulation of the residual equations, and construction of the final approximate solution. Worked examples are used to demonstrate how the method performs in practice and how accuracy improves with higher-order approximations, helping you build strong intuition for applying the collocation method to boundary value problems and real-world engineering models.
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