Solving Equations Using Differential Transformation Method

Differential transformation method can be used to solve differential equation even integro-differential equations.

Differential transformation is a method that applies the Taylor expansion of the function. For an arbitrary function f(x), we can Taylor expand it

(1)f(x)=n=0NF(n)(xx0)n,

where F(n) is the coefficient of Taylor expansion. By using the definition, we can explore the properties of this transformation from function f(x) to F(n).

Table of DTM. From Munganga, J. M. W., Mwambakana, J. N., Maritz, R., Batubenge, T. a., & Moremedi, G. M. (2014). Introduction of the differential transform method to solve differential equations at undergraduate level. International Journal of Mathematical Education in Science and Technology, 45(5), 781–794. http://doi.org/10.1080/0020739X.2013.877609

Table of DTM. From Munganga, J. M. W., Mwambakana, J. N., Maritz, R., Batubenge, T. a., & Moremedi, G. M. (2014). Introduction of the differential transform method to solve differential equations at undergraduate level. International Journal of Mathematical Education in Science and Technology, 45(5), 781–794. http://doi.org/10.1080/0020739X.2013.877609

For more references about this topic, read

  1. Munganga, J. M. W., Mwambakana, J. N., Maritz, R., Batubenge, T. a., & Moremedi, G. M. (2014). Introduction of the differential transform method to solve differential equations at undergraduate level. International Journal of Mathematical Education in Science and Technology, 45(5), 781–794. http://doi.org/10.1080/0020739X.2013.877609
  2. Arikoglu, A., & Ozkol, I. (2008). Solutions of integral and integro-differential equation systems by using differential transform method. Computers and Mathematics with Applications, 56(9), 2411–2417. http://doi.org/10.1016/j.camwa.2008.05.017

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L Ma (2016). 'Solving Equations Using Differential Transformation Method', Datumorphism, 10 April. Available at: https://datumorphism.leima.is/til/math/differential-transformation-method-solving-equations/.