Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory Solutions

Abstract

In this paper, we proposed a trigonometrically-fitted fifth order four-step predictor-corrector method based on the four-step Adams-Bashforth method as predictor and five-step Adams-Moulton method as corrector to solve linear ordinary differential equations with oscillatory solutions. This method is constructed which exactly integrate initial value problems whose solutions can be expressed as linear combinations of the set functions {sin(υx),cos(υx)} with υ ∈ R, where v represents an approximation of the frequency of the problem. The frequency will be used in the method to raise the accuracy of the solution. Stability of the proposed method is examined and the corresponding region of stability is depicted. The new fifth algebraic order trigonometrically-fitted predictor-corrector method is applied to solve the initial value problems whose solutions involved trigonometric functions. Numerical results presented proved that the prospective method is more efficient than the widely used methods for the numerical solution of linear ordinary differential equations with oscillating solutions.