Two New WRM Weight Functions based on Galerkin, Least squared, and Subdomain Methods for Solving 1D ODEs

Not all differential equations have exact analytical solutions; sometimes an approximate solution will have to do. Other times, an approximate solution may be more useful than an exact solution. Some problems may have a simple approximation that indicates some characteristic behavior or allows numerical values to be obtained rather than laborious analytical solutions. One of these numerical methods is weighted residual methods in which the results depend upon weight function. In this paper two new weight functions based on Galerkin, Sub-Domains, and Least squares are provided to solve one-dimensional ordinary differential equations and results and errors are compared to that of analytical solution and the base weight functions themselves.

کلیدواژه ها:

Weight functions ، ODE solution ، Galerkin ، WRM ، least squared