On Morgan-Voyce Polynomials Approximation For Linear Differential Equations

Year 2014, Volume 2, 2014, 1 - 10, 26.05.2016

Özgül İlhan Niyazi Şahin

Abstract

In this paper, a matrix method for approximately solving certain linear differential equations is presented. This method is called Morgan-Voyce matrix method and converts a linear differential equation into a matrix equation. Then, the equation reduces to a matrix equation corresponding to a system of linear algebraic equations with unknown Morgan-Voyce coefficients. The examples are included to demonstrate the applicability of the technique.

Keywords

Morgan-Voyce polynomials, linear differential equations, collocation method

References

• Ş. Yüzbaşı, N. Şahin, M. Sezer. Numerical solutions of systems of linear Fredholm integrodifferential equations with Bessel Polynomial bases. Computers&Mathematics with Applications, pp. 3079-3096, 22 April 2011.
• M. N. S. Swamy. Further properties of Morgan-Voyce Polynomials. Fibonacci Quarterly, Vol. 6, No. 2, pp. 167-175, Apr. 1968.
• H. H. Sorkun, S. Yalçınbas. Approximate solutions of linear Volterra integral equation systems with variable coefficients. Appl. Math. Modell., doi:10.1016/j.apm.2010.02.034., (2010).
• A. Akyüz-Daşçıoğlu, M. Sezer. Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations. J. Franklin Ins., vol. 342, pp. 688-701, (2005).
• M. Sezer and A. Akyüz-Daşcıoğlu. A Taylor method for numerical solution of generalized pantograph equations with linear functional argument. J. Comput. Appl. Math., vol. 200, pp. 217-225, (2007).
• M. Sezer. A method for the approximate solution of the second order linear differential equations in terms of Taylor polynomials. Int J Math Educ Sci Technol., vol. 27, pp. 821-834, (1996).
• M. Sezer, S. Yalçınbaş, and N. Şahin Approximate solution of multi-pantograph equation with variable coefficients J Comput Appl Math, vol. 214, pp. 406-416, (2008).