# DERIVATION AND IMPLEMENTATION OF A THREE-STEP HYBRID BLOCK ALGORITHM (TSHBA) FOR DIRECT SOLUTION OF LINEAR AND NONLINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

## Authors

• OLUSOLA EZEKIEL ABOLARIN Mathematics Department, Federal University Oye-Ekiti, Ekiti State
• Bamikole Gbenga Ogunware Mathematics and Statistics Department, Joseph Ayo Babalola University, ikeji Arakeji, Osun State, Nigeria
• A. F ADEBISI DEPARTMENT OF MATHEMATICAL SCIENCES, OSUN STATE UNIVERSITY, OSOGBO
• S. O AYINDE Department of Mathematics, Ekiti State University, Ado-Ekiti, Ekiti State

## Keywords:

Power Series, Block method, Implicit, Interpolation and Collocation, Linear and Non-linear Ordinary Differential Equations (ODEs)

## Abstract

The development and application of an implicit hybrid block method for the direct solution of second order ordinary differential equations with given initial conditions is shown in this research. The derivation of the three-step scheme was done through collocation and interpolation of power series approximation to give a continuous linear multistep method. The evaluation of the continuous method at the grid and off grid points formed the discrete block method. The basic properties of the method such as order, error constant, zero stability, consistency and convergence were properly examined. The new block method produced more accurate results when compared with similar works carried out by existing authors on the solution of linear and non-linear second order ordinary differential equations.

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2021-01-17

## How to Cite

ABOLARIN , O. E., Ogunware, B. G., ADEBISI , A. F., & AYINDE , S. O. (2021). DERIVATION AND IMPLEMENTATION OF A THREE-STEP HYBRID BLOCK ALGORITHM (TSHBA) FOR DIRECT SOLUTION OF LINEAR AND NONLINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS. FUDMA JOURNAL OF SCIENCES, 4(4), 477 - 483. https://doi.org/10.33003/fjs-2020-0404-491

## Section

Research Articles