Trigonometrically fitted block Numerov type method for y″=f(x, y, y')

Trigonometrically fitted block Numerov type method for y″=f(x, y, y')

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Article ID: iaor2013593
Volume: 62
Issue: 1
Start Page Number: 13
End Page Number: 26
Publication Date: Jan 2013
Journal: Numerical Algorithms
Authors: , ,
Keywords: differential equations
Abstract:

A trigonometrically fitted block Numerov type method (TBNM), is proposed for solving y′′ = f(x, y, y′) directly without reducing it to an equivalent first order system. This is achieved by constructing a continuous representation of the trigonometrically fitted Numerov method (CTNM) and using it to generate the well known trigonometrically fitted Numerov method (TNUM) and three new additional methods, which are combined and applied in block form as simultaneous numerical integrators. The stability property of the TBNM is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.

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