Barycentric Rational Interpolation For Differential Equation

The Burgers equation with regard to time and space variables is fundamental in hydromechanics. The classic methods for partial differential equations include FEM, FDM, and spectral method. In this paper, we apply collocation method in solving the Burgers equation and take Floater-Hormann type functions as the basis function.Chapter1is devoted to the introduction of hydromechanics, collocation method and rational interpolation. Composite rational interpolation presented by Floater and Hormann is also included. We use Berrut and Floater-Hormann barycentric interpolation to approximate Runge function and estimate the error. In addition, we also involve something about Lebesgue constant.In Chapter2, we first introduce the algorithm for computing the differential matrix of barycentric Lagrange interpolation. Then, we deal with boundary conditions by using the substitution method. Finally, this section is ended up with an example of ODE with boundary conditions.We, in Chapter3, present the background of Burgers equation and give the algorithm for solving this equation based on collocation method with equally spaced nodes. Numerical tests manifest this approach is efficient.Equidistant nodes is frequently used in real life, and the use of equidistant nodes to interpolation approximation is a reality in practical problems. This paper use Floater-Hormann interpolation on equidistant to approximate the unknown function and use it as basis function for solving differential equations.