Abstract
This paper presents the approximate solution of higher order boundary value problems by differential transform method. Two examples are considered to illustrate the efficiency of this method. The results converge rapidly to the exact solution and are shown in tables and graphs.
Highlights
Studies showed that higher order boundary value problems arise in the areas of fluid dynamics, hydrodynamics and hydromagnetic stability and other applied sciences
Sixth order boundary value problems occur in astrophysics and it has attracted the attention of researchers like Wazwaz (2001) who investigated it using modified decomposition method, He (2003) used variational approach method and Erturk (2007) approached it via differential transformation method
Seventh order boundary value problems that arise in modeling induction motors with two rotor circuits was considered by Siddiqi et al (2012) while eight-order boundary value problem which occur in hydrodynamic and hydromagnetic stability was studied by Siddiqi et al (1996) and Mohammad-Jawad (2010)
Summary
Studies showed that higher order boundary value problems arise in the areas of fluid dynamics, hydrodynamics and hydromagnetic stability and other applied sciences. Sixth order boundary value problems occur in astrophysics and it has attracted the attention of researchers like Wazwaz (2001) who investigated it using modified decomposition method, He (2003) used variational approach method and Erturk (2007) approached it via differential transformation method. Other authors who have studied higher order boundary value problems include Wazwaz (2000), Othman et al (2010) and Mohyud-Din (2010). The differential transform method is applied in this work to solve boundary value problems of ninth and twelfth orders. This method was proposed by Zhou (1986). Some authors who have adopted this method include, Opanuga et al (2014) on systems of ordinary differential equations, Opanuga et al (2015) applied it in numerical solution of two-point boundary value problems, Edeki et al (2014) analyzed linear and nonlinear differential equations and Edeki et al (2015), in transformed Cauchy-Euler equidimensional equations of homogenous type
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