A HYBRID BLOCK METHOD FOR DIRECT SOLUTION OF GENERAL FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

Many problems in applied sciences and engineering, such as static deflection of a uniform beam, fluid
dynamics, neural networks, electric circuits, and the illposed problem of a beam on elastic foundation often
result to fourth-order initial value problem of ordinary differential equations (ODEs). In this study a direct
solution for the general fourth-order initial value problems of (ODEs) was derived using Linear Multi-step
Method. Power series and its derivatives are adopted as basis function and differential for the purpose of
interpolation and collocation respectively. This interpolation and collocation are carried out at selected
nodal and off-nodal points to generate a set of linear equations. Solving these equations give the values for
the unknown coefficient parameters to be used to determine the required continuous method after necessary
simplification. The additional methods are obtained for the implementation of the main methods in block
mode. The basic properties of the hybrid methods is established to confirm their usability, accuracy and
efficiency. Accuracy and efficiency of the methods is determined by applying the derived methods to solve
linear and non-linear test problems. The results obtained is compared with those of cited methods in
literature