APPROXIMATE SOLUTION OF SECOND-ORDER BOUNDARY-VALUE PROBLEM USING THE RITZ METHOD
Keywords:
ordinary differential equation, boundary value problem, variational methods, Ritz method, approximate solution, basis functions, algebraic system.Abstract
This article considers the problem of obtaining an approximate solution of a boundary value problem for a second-order linear ordinary differential equation using the Ritz method. The given differential equation is transformed into a self-adjoint form using an integrating factor, and the corresponding variational functional is constructed. A particular function satisfying the boundary conditions and basis functions satisfying homogeneous boundary conditions are selected. For the case n=4, an approximate solution is constructed and a system of algebraic equations with respect to the unknown coefficients is obtained. The resulting system is solved using the Gaussian elimination method, and an approximate solution of the problem is determined.
