APPROXIMATE SOLUTION OF BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATIONS USING THE COLLOCATION METHOD
Keywords:
ordinary differential equation, boundary value problem, approximate solution, collocation method, basis functions, algebraic system, internal points.Abstract
In this article, the problem of obtaining an approximate solution of a boundary value problem for a second-order linear ordinary differential equation using the collocation method is considered. In constructing the approximate solution, a particular function satisfying the given boundary conditions and basis functions corresponding to homogeneous boundary conditions are chosen. For the case n=4 the differential equation is required to be satisfied at four internal collocation points, which leads to a system of algebraic equations with respect to unknown coefficients. By solving this system, an approximate analytical solution of the problem is obtained. The obtained results show that the collocation method is one of the effective and practically convenient methods for solving boundary value problems.
