A Continuous Chebyshevian Hybrid Method for Direct Solution of Second Order Differential Equations
F. O. Obarhua
Department of Mathematical Sciences, The Federal University of Technology, P.M.B 704, Akure, Nigeria.
B. Adamu *
Department of Basic Sciences, Federal Polytechnic P.M.B 13, Auchi, Edo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper develops a hybrid linear multistep scheme based on Chebyshev polynomials for the direct solution of general second-order ordinary differential equations. The basis function is interpolated at grid points as well as selected off-grid points, and the resulting differential equation is collocated at every grid point. The derived method is shown to be continuous, consistent, symmetric, and zero-stable, and numerical experiments indicate that it produces more accurate results than several existing methods.
Keywords: Linear multistep method, hybrid point, chebyshev polynomial, collocation and interpolation, predictor-corrector method