A PREDICTOR- CORRECTOR HYBRID METHOD FOR DIRECT SOLUTION OF MODELED REAL LIFE PROBLEMS OF SECOND ORDER ODES
DOI:
https://doi.org/0.33003/fjs-2026-1004-4765Keywords:
linear multistep method, Hybrid point, chebyshev polynomial, collocation and interpolation, predictor-corrector methodAbstract
This paper develops a chebyshevian hybrid linear multi step method to solve general second order ordinary differential equations (O.D.Es). The development of the method utilized the chebyshev polynomial of the first kind as the basis function for the approximation solution. The interpolation of the bais function was done at both grid and off grid points. While the differential systems are colocated at all grid points for step number k=2 . The require continuous hybrid method is produced by the substitution of the unknown parameters in to the basis function and the simplication of the resulting equations. The inherent demerit of predictor methods of lower order is circumvented by the driving predictors of the same order with the methods. The methods were applied to solve real life second order initial value problems directly. The errors in the results obtained were compared to those from the existing methods. The comparison shows a better performance than the existing methods.
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Copyright (c) 2026 Friday Oghenerukevwe Obarhua, Adelegan Momoh Lukman, Adamu Bala
This work is licensed under a Creative Commons Attribution 4.0 International License.
