Revista de Matemáticas Aplicadas y Computacionales

One Step, Three Hybrid Block Predictor-Corrector Method for the Solution of y''' = f (x, y, y ', y'')

Abstract

Adesanya A Olaide, Fasansi M Kolawole and Odekunle M Remilekun

We developed a one step-three hybrid point constant order predictor corrector method for the solution of general third order initial value problems. The method was developed using method of interpolation and collocation of power series approximate solution to generate a continuous linear multistep method which was evaluated at some selected grid point to give the discrete linear multistep method. The predictors are implemented in block method while the corrector gave the solution at an overlapping interval. The basic properties of both the corrector and the predictors were investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The efficiency of the derived method was tested on some numerical examples and found to compete favourably with the existing methods.