A Semi-Analytical Method for Solutions of a Certain Class of Second Order Ordinary Differential Equations
Abstract: This paper presents the theory and applications of a new computational technique referred to as Differential Transform Method (DTM) for solving second order linear ordinary differential equations, for both homogeneous and nonhomogeneous cases. For the robustness and efficiency of the method, four examples are considered. The results indicate that the DTM is reliable and accurate when compared to the exact solutions of the solved problems.
Cite this paper: Edeki, S. , Okagbue, H. , Opanuga, A. and Adeosun, S. (2014) A Semi-Analytical Method for Solutions of a Certain Class of Second Order Ordinary Differential Equations. Applied Mathematics, 5, 2034-2041. doi: 10.4236/am.2014.513196.
References

[1]   Zhou, J.K. (1986) Differential Transformation and its Applications for Electrical Circuits. Huazhong University Press, Wuhan.

[2]   Chen, C.L. and Liu, Y.C. (1988) Solution of Two Point Boundary Value Problems Using the Differential Transformation Method. Journal of Optimization Theory and Applications, 99, 23-35.
http://dx.doi.org/10.1023/A:1021791909142

[3]   Ayaz, F. (2004) Application of Differential Transform Method to Differential-algebraic Equations. Applied Mathematics and Computation, 152, 649-657.
http://dx.doi.org/10.1016/S0096-3003(03)00581-2

[4]   Kangalgil, F. and Ayaz, F. (2009) Solitary Wave Solutions for the kdv and mkdv Equations by Differential Transform Method. Chaos, Solitons and Fractals, 41, 464-472.
http://dx.doi.org/10.1016/j.chaos.2008.02.009

[5]   Batiha, K. and Batiha, B. (2011) A New Algorithm for Solving Linear Ordinary Differential Equations. World Applied Sciences Journal, 15, 1774-1779.

[6]   Thongmoon, M. and Pusjuso, S. (2010) The Numerical Solutions of Differential Transform Method and the Laplace Transform Methods for a System of Differential Equations. Nonlinear Analysis: Hybrid Systems, 4, 425-431.
http://dx.doi.org/10.1016/j.nahs.2009.10.006
www.elsevier.com/locate/nahs

[7]   Ravi Kanth, A.S.V. and Aruna, K. (2009) Differential Transform Method for Solving the Linear and Nonlinear Klein-Gordon Equation. Computer Physics Commmunications, 180, 708-711.
http://dx.doi.org/10.1016/j.cpc.2008.11.012

[8]   Chang, S.H. and Chang, I.L. (2008) A New Algorithm for Calculating One-Dimensional Differential Transform of Nonlinear Functions. Applied Mathematics and Computation, 195, 799-808.
http://dx.doi.org/10.1016/j.amc.2007.05.026

[9]   Adomian, G. (1994) Solving Frontier Problems of Physics. The Decomposition Method. Springer, New York.

[10]   Ibijola, E.A. and Adegboyegan, B.J. (2008) On the Theory and Application of Adomian Decomposition Method for Solution of Second Order ODEs. Pacific Journal of Science and Technology, 9, 357-362.

[11]   Shousa, D.-H. and He, J.-H. (2008) Beyond Adomian Method: The Variational Iteration Method for Solving Heat-Like and Wave-Like Equations with Variable Coefficients. Physics Letters A, 372, 233-237.
http://dx.doi.org/10.1016/j.physleta.2007.07.011

[12]   He, J.-H. (2007) Variational Iterative Method—Some Recent Results and New Interpretations. Journal of Computational and Applied Mathematics, 207, 3-17.
http://dx.doi.org/10.1016/j.cam.2006.07.009

[13]   Catal, S. (2012) Some of Semi Analitical Methods for Blasius Problem. Applied Mathematics, 3, 727-728.
http://dx.doi.org/10.4236/am.2012.37106

[14]   Arikoglu, A. and Ozkol, I. (2005) Solution of Boundary Value Problems for Integro-Differential Equations by Using Transform Method. Applied Mathematics and Computation, 168, 1145-1158.
http://dx.doi.org/10.1016/j.amc.2004.10.009

[15]   Odibat, Z. (2008) Differential Transform Methods for Solving Volterra Integral Equations with Separable Kernels. Mathematical and Computer Modelling, 48, 1144-1146.
http://dx.doi.org/10.1016/j.mcm.2007.12.022

Top