A Summary Result on Second Order Linear Differential Equations with Variable Coefficients using Adomian Decomposition Method and Power Series Method
Grace N. Echezona, Francis O. Nwawuru
Abstract
This paper considers two methods with series solutions to second order linear differential equations with variable coefficients. These series solutions are given by the Adomian decomposition method and the Power series method. The two methods provide approximate solutions with their techniques being different and unique. We will take some examples to illustrate the techniques of these mentioned methods and compare the results obtained. Included in the examples to be considered, is a case where none of the coefficients of the variables is zero.
Keywords
A domian decomposition method
power series method
linear differential
equations
variable coefficients
series solutions.
References
[1]. Wilmer, A. & Costa, G. B. (2008), Solving second order differential equations with
variable coefficients, International journal of mathematical edu. in sci and tech., 238 –
243.
[2]. Wazwaz, A. – M. (1998), A comparison between Adomian decomposition method and
Taylor series method solution, Appl Math. Comput. 97, 37 – 44.
[3]. Adomian, G. (1988), A review of the decomposition method in applied Mathematics,
Journal of mathematical analysis and applications, 135, 501 – 544.
[4]. Nhawu, G., Mafuta, P. & Mushanyu, J. (2016), The Adomian decomposition method for
numerical solution of first order differential equations, J. Math. Comput. Sci., 6, No 3,
307 – 314.
[5]. Dabwan, N. M. & Hasan Y. Q. (2020), Solving second order ordinary differential
equations using new modified Adomian method, Scientific journal 9, no 3, 937 – 943.
variable coefficients, International journal of mathematical edu. in sci and tech., 238 –
243.
[2]. Wazwaz, A. – M. (1998), A comparison between Adomian decomposition method and
Taylor series method solution, Appl Math. Comput. 97, 37 – 44.
[3]. Adomian, G. (1988), A review of the decomposition method in applied Mathematics,
Journal of mathematical analysis and applications, 135, 501 – 544.
[4]. Nhawu, G., Mafuta, P. & Mushanyu, J. (2016), The Adomian decomposition method for
numerical solution of first order differential equations, J. Math. Comput. Sci., 6, No 3,
307 – 314.
[5]. Dabwan, N. M. & Hasan Y. Q. (2020), Solving second order ordinary differential
equations using new modified Adomian method, Scientific journal 9, no 3, 937 – 943.
