Solving linear and nonlinear initial value problems by the projected differential transform method. (English) Zbl 1205.65205

Jang, Bongsoo

Comput. Phys. Commun. 181, No. 5, 848-854 (2010).

Summary: We propose a novel computational algorithm for solving linear and nonlinear initial value problems by using the modified version of differential transform method (DTM), which is called the projected differential transform method (PDTM). The PDTM can be easily applied to the initial value problems with less computational work. For the several illustrative examples, the computational results are compared with those obtained by many other methods; the Adomian decomposition, the variational iteration and the spline method. For all examples, the PDTM provides exact solutions. It has been shown that the PDTM is a reliable algorithm in obtaining analytic as well as approximate solution for the initial value problems.

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
34A30	Linear ordinary differential equations and systems
34A34	Nonlinear ordinary differential equations and systems

Keywords:

Taylor series; initial value problems; differential transform method; numerical examples; algorithm; Adomian decomposition; variational iteration; spline method

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