A THREE-STEP INTERPOLATION TECHNIQUE WITH PERTURBATION TERM FOR DIRECT SOLUTION OF THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS (FUDMA JOURNAL OF SCIENCES, 2021)
In this paper, we developed a new three-step method for numerical solution of third order ordinary differential equations. Interpolation and collocation methods were used by choosing interpolation points at  steps points using power series, while collocation points at  step points, using a combination of powers series and perturbation terms gotten from the Legendre polynomials, giving rise to a polynomial of degree and equations. All the analysis on the method derived shows that it is zero-stable, convergent and the region of stability is absolutely stable. Numerical examples were provided to test the performance of the method. Results obtained when compared with existing methods in the literature, shows that the method is accurate and efficient
Keywords: Three-step Interpolation technique; Legendre Polynomial; Perturbation Term; Third-order ODEs; Convergent; Power Series; Absolutely stable.