Weighted Residual Methods

• Published in: Advanced Numerical and Semi-Analytical Methods for Differential Equations pp. 31 - 43
• Main Authors: Chakraverty, Snehashish, Mahato, Nisha, Karunakar, Perumandla, Dilleswar Rao, Tharasi
• Format: Book Chapter
• Language: English
• Published: United States Wiley 2019; John Wiley & Sons, Incorporated; John Wiley & Sons, Inc
• Edition: 1
• Subjects: boundary value problems; collocation method; Galerkin method; least‐square method; ordinary differential equations; subdomain method; weighted residual methods; Boundary conditions; Shape; IEEE Sections; Force; Method of moments; Standards
• ISBN: 9781119423423; 1119423422
• DOI: 10.1002/9781119423461.ch3

Weighted residual method (WRM) is an approximation technique in which solution of differential equation is approximated by linear combination of trial or shape functions having unknown coefficients. The approximate solution is then substituted in the governing differential equation resulting in error or residual. Finally, in the WRM the residual is forced to vanish at average points or made as small as possible depending on the weight function in order to find the unknown coefficients. The authors illustrate various WRMs, viz. collocation, subdomain, least‐square, and Galerkin methods applied for solving ordinary differential equations subject to boundary conditions. They also check the efficiency of various WRMs by comparing the solution obtained using collocation, subdomain, least‐square, and Galerkin methods for the boundary value problems. Lastly, the authors present few exercise problems for self‐validation.