Numerical Solution for High-Order Linear Complex Differential Equations By Hermite Polynomials

Year 2017, Volume: 7 Issue: 4, 189 - 201, 31.12.2017

Faruk Düşünceli , Ercan Çelik

Abstract

In this paper, the numerical solutions of complex differential equations are provided by the Hermite

Polynomials and carried on two problems. As a result, the exact solutions and numerical one’s have compared by

tables and graphs that the method is practical, reliable and functional.

Keywords

Hermite polynomials, linear complex differential equations, numerical solution

Yüksek Mertebeden Lineer Kompleks Diferansiyel Denklemlerin Hermite Polinomları ile Nümerik Çözümleri

Abstract

Bu makalede lineer kompleks diferansiyel denklemleri hermite polinomları vasıtasıyla nümerik çözümünü

sağladık ve iki test problemine uyguladık. Tam çözümler ile nümerik çözümleri tablo ve grafikler ile karşılaştırdık.

Sonuç olarak metodumuzun güvenilir, pratik ve kullanışlı olduğunu gördük.

Keywords

Hermite polinomları, lineer kompleks diferansiyel denklemler, nümerik çözüm

References

• Düşünceli F, Çelik E, 2015. An effective tool: Numerical solutions by Legendre polynomials for high-order linear complex differential equations. British Journal of Applied Science &Technology, 8(4): 348-355.
• Düşünceli F, Çelik E, 2017. Fibonacci matrix polynomial method for linear complex differential equations. Asian Journal of Mathematics and ComputerResearch, 15(3): 229-238.
• Gülsu M, Gürbüz B, Öztürk Y, Sezer M, 2011.Laguerre polynomial approach for solving linear delay difference equations.Applied Mathematics and Computation, 217:6765–6776.
• Sezer M, Yalçınbaş S, 2009.A collocation method to solve higher order linear complex differential equations in rectangular domains.Numerical Methods for Partial Differential Equations, 26:596–611.
• Tohidi E, 2012. Legendre approximation for solving linear HPDEs and comparison with Taylor and Bernoulli matrix methods.Applied Mathematics, 3:410–416.
• Yüzbaşı S, Aynıgül M, Sezer M, 2011.A collocation method using Hermite polynomials for approximate solution of pantograph equations.Journal of the Franklin Institute, 348:1128–1139.
• Yüzbası S, Şahin N, Gülsu M, 2011. A collocation approach for solving a class of complex differential equations in elliptic domains.Journal of Numerical Mathematics, 19: 225–246.