A CLASS OF HYBRID BLOCK INTEGRATORS FOR INITIAL VALUE PROBLEMS OF FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this research works, the development of a class of hybrid block integrators for initial value problems (ivps) of fourth order ordinary differential equations (odes) is discussed. One-step self starting continuous hybrid block integrators with better accuracy and larger interval of absolute stability are developed for direct solutions of linear and non-linear fourth order odes without reduction to system of the first order odes. The differential system obtained from the basis function and the approximate solution to the problem were collocated and interpolated respectively at both the grid and off-grid points. The resulting systems of equations were solved to obtain values of the unknown parameters. Substituting the values of these parameters and evaluating the results at the different grid and off-grid points yield the required discrete schemes. The methods obtained were then implemented in block form. The methods were tested for consistency, zero stability, convergence and Absolute stability. Accuracy of the methods was determined with some test problems and the results obtained were found to be better in accuracy than some existing methods.