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Application of a Two-Step Third-Derivative Block Method for Starting Numerov Method
International Journal of Theoretical and Applied Mathematics
Volume 3, Issue 1, February 2017, Pages: 30-35
Received: Sep. 26, 2016; Accepted: Dec. 10, 2016; Published: Jan. 12, 2017
Authors
Oluwaseun Adeyeye, Department of Mathematics, Universiti Utara Malaysia, Kedah, Malaysia
Zurni Omar, Department of Mathematics, Universiti Utara Malaysia, Kedah, Malaysia
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Abstract
Numerov method is one of the most widely used algorithms in physics and engineering for solving second order ordinary differential equations. The numerical solution of this method has been improved by different authors by using different starting formulas but in recent years, there has been a dearth in that trend which informed the introduction of a two-step third-derivative block method in this paper to start Numerov method with the aim of getting better results than previous approaches. The selection of the steplength as two is to have a uniform basis for comparison with other existing two-step starting formula in literature. Although, the accuracy of the two-step method adopted in this article was enhanced by the introduction of higher derivative. Hence, this paper presents a two-step third-derivative block method which displayed better accuracy when adopted for starting Numerov method as shown in the numerical results. Thus, the third-derivative block method, as a starting formula, is seen to be quite suitable for starting Numerov method when applied to physical models.
Keywords
Numerov, Two-Step, Third-Derivative, Block Method, Second Order, Initial Value Problems
Oluwaseun Adeyeye, Zurni Omar, Application of a Two-Step Third-Derivative Block Method for Starting Numerov Method, International Journal of Theoretical and Applied Mathematics. Vol. 3, No. 1, 2017, pp. 30-35. doi: 10.11648/j.ijtam.20170301.15
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