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Mean Square Solutions of Second-Order Random Differential Equations by Using the Differential Transformation Method

DOI: 10.4236/ojapps.2016.64028, PP. 287-297

Keywords: Random Differential Equations, Stochastic Differential Equation, Differential Transformation Method

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Abstract:

The differential transformation method (DTM) is applied to solve the second-order random differential equations. Several examples are represented to demonstrate the effectiveness of the proposed method. The results show that DTM is an efficient and accurate technique for finding exact and approximate solutions.

References

[1]  Chiles, J. and Delfiner, P. (1999) Geostatistics: Modelling Spatial Uncertainty. John Wiley, New York.
[2]  Cortes, J.C., Jodar, L. and Villafuerte, L. (2009) Random Linear-Quadratic Mathematical Models: Computing Explicit Solutions and Applications. Mathematics and Computers in Simulation, 79, 2076-2090. http://dx.doi.org/10.1016/j.matcom.2008.11.008
[3]  Soong, T.T. (1973) Random Differential Equations in Science and Engineering. Academic Press, New York.
[4]  Cortés, J.C., Jódar, L. and Villafuerte, L. (2007) Mean Square Numerical Solution of Random Differential Equations: Facts and Possibilities. Computers and Mathematics with Applications, 53, 1098-1106.
http://dx.doi.org/10.1016/j.camwa.2006.05.030
[5]  Cortés, J.C., Jódar, L. and Villafuerte, L. (2007) Numerical Solution of Random Differential Equations: A Mean Square Approach. Mathematical and Computer Modelling, 45, 757-765.
http://dx.doi.org/10.1016/j.mcm.2006.07.017
[6]  Cortés, J.C., Jódar, L. and Villafuerte, L. (2007) Mean Square Numerical Solution of Random Differential Equations: Facts and Possibilities. Computers and Mathematics with Applications, 53, 1098-1106.
http://dx.doi.org/10.1016/j.camwa.2006.05.030
[7]  Cortés, J.C., Jódar, L. and Villafuerte, L. (2009) Random Linear Quadratic Mathematical Models: Computing Explicit Solutions and Applications. Mathematics and Computers in Simulation, 79, 2076-2090.
http://dx.doi.org/10.1016/j.matcom.2008.11.008
[8]  Villafuerte, L., Braumann, C.A., Cortés, J.C. and Jódar, L. (2010) Random Differential Operational Calculus: Theory and Applications. Computers & Mathematics with Applications, 59, 115-125.
[9]  Calbo, G., Cortés, J.C. and Jódar, L. (2010) Mean Square Power Series Solution of Random Linear Differential Equations. Computers and Mathematics with Applications, 59, 559-572.
http://dx.doi.org/10.1016/j.camwa.2009.06.007
[10]  Cortés, J.C., Jódar, L., Villanueva, R.-J. and Villafuerte, L. (2010) Mean Square Convergent Numerical Methods for Nonlinear Random Differential Equations. Lecture Notes in Computer Science, 5890, 1-21.
http://dx.doi.org/10.1007/978-3-642-11389-5_1
[11]  Cortés, J.C., Jódar, L., Villafuerte, L. and Company, R. (2011) Numerical Solution of Random Differential Models. Mathematical and Computer Modelling, 54, 1846-1851.
http://dx.doi.org/10.1016/j.mcm.2010.12.037
[12]  Khudair, A.R., Ameen, A.A. and Khalaf, S.L. (2011) Mean Square Solutions of Second-Order Random Differential Equations by Using Adomian Decomposition Method. Applied Mathematical Sciences, 5, 2521-2535.
[13]  Khudair, A.R., Ameen, A.A. and Khalaf, S.L. (2011) Mean Square Solutions of Second-Order Random Differential Equations by Using Variational Iteration Method. Applied Mathematical Sciences, 5, 2505-2519.
[14]  Khalaf, S.L. (2011) Mean Square Solutions of Second-Order Random Differential Equations by Using Homotopy Perturbation Method. International Mathematical Forum, 6, 2361-2370.
[15]  Zhou, J.K. (1986) Differential Transformation and Its Applications for Electrical Circuits. Huazhong University Press, Wuhan.
[16]  Lo′eve, M. (1963) Probability Theory. Van Nostrand, Princeton, New Jersey.
[17]  Wong, E. and Hajek, B. (1985) Stochastic Processes in Engineering System. Springer Verlag, New York. http://dx.doi.org/10.1007/978-1-4612-5060-9

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