A block hybrid integrator for numerically solving fourth-order Initial Value Problems

摘要

A Linear Multistep Hybrid Block method with four intra-step grid points is presented for approximating directly the solution of fourth order Initial Value Problems (IVPs). Multiple Finite Difference formulas are derived and combined in a block formulation to form a numerical integrator that provides direct solution to fourth order IVPs over sub-intervals. The properties and convergence of the proposed method are discussed. The superiority of this method over existing methods is established numerically on different test problems.