Adams Type Hybrid Block Methods Associated with Chebyshev Polynomial for the Solution of Ordinary Differential Equations

The new Hybrid Adams type Block Methods (HATBMs) for step length k=2,3 and 4 were developed for the solution of first order ordinary differential equations. Collocation and interpolation of Chebyshev polynomial approximation were adopted to derive some implicit linear multi-step methods at different values of k. Analysis of all the methods show that they were consistent, zero stable and convergent. All the newly constructed methods were demonstrated with numerical experiments to ascertain their level of convergence.