A BACKWARD DIFFERENTIATION FORMULA FOR THIRD-ORDER INITIAL OR BOUNDARY VALUES PROBLEMS USING COLLOCATION METHOD

Subject Areas : Numerical Analysis

GAFAR  TIAMIYU ¹ (Department of Mathematics, Federal University of Technology, Minna, Nigeria)
Abosede  COLE ² (Department of Mathematics, Federal University of Technology, Minna, Nigeria)
KHADEEJAH  AUDU ³ (Department of Mathematics, Federal University of Technology, Minna, Nigeria)

Received: 2021-06-19 Accepted : 2021-09-19 Published : 2021-06-01

Keywords: Boundary value problems, Initial value problems, Third Order ODE, Backward Differentiation Formula, Hybrid Linear Multistep,

Abstract :

We propose a new self-starting sixth-order hybrid block linear multistep method using backward differentiation formula for direct solution of third-order differential equations with either initial conditions or boundary conditions. The method used collocation and interpolation techniques with three off-step points and five-step points, choosing power series as the basis function. The convergence of the method is established, and three numerical experiments of initial and boundary value problems are used to demonstrate the efficiency of the proposed method. The numerical results in Tables and Figures show the efficiency of the method. Furthermore, the numerical method outperformed the results from existing literature in terms of accuracy as evident in the results of absolute errors produced.

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