Block Hybrid Method for the Numerical solution of Fourth order Boundary Value Problems.

Abstract

[EN]A linear Multistep Block Hybrid Method with four off-grid points is presented for the direct approximation of the solution of fourth order Boundary Value Problems. Multiple Finite Difference formulas are derived and grouped into a unique block to form a numerical integrator to solve directly the fourth order problem, without the need to reduce it previously to a first-order system. The convergence of the proposed method is discussed. The superiority of this method over existing methods is established numerically considering different problems that have appeared in the literature.