Abstract
The weighted residual method (WRM) is a technique for estimating the solution of a differential equation with unknown coefficients using a linear combination of trial or shape functions. The governing differential equation is then solved using the approximate solution, providing an error or residual. Finally, the residual is pushed to vanish at average points or made as small as possible to find the unknown coefficients depending on the weight functions. This chapter uses various WRMs, such as collocation, least-squares, and Galerkin methods, to solve fractional-order ordinary differential equations with boundary conditions. We also compare the solutions derived by collocation, least-square, and Galerkin techniques with exact solutions to determine the efficacy of various WRMs. This chapter also includes solution graphs for different values of alpha and error plots.
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