Taylor series method for solving differential equations represents a non-traditional way of solving differential equations. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with the special case of wave partial differential equation - Telegraph equation and with the modeling of the behavior of electrical signals on a telegraph line. Experiments with large systems of ordinary differential equations on homogenous and non-homogenous wiring (about 1500 equations) are analyzed. The possibility of accelerating the computations in GPU using nVidia CUDA is outlined. The results are compared with those obtained by world standards MatLab and Maple software.

Taylor series method for solving differential equations represents a non-traditional way of solving differential equations. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with the special case of wave partial differential equation - Telegraph equation and with the modeling of the behavior of electrical signals on a telegraph line. Experiments with large systems of ordinary differential equations on homogenous and non-homogenous wiring (about 1500 equations) are analyzed. The possibility of accelerating the computations in GPU using nVidia CUDA is outlined. The results are compared with those obtained by world standards MatLab and Maple software. (en)

Telegraph equation, Differential equations, Modern Taylor Series Method (en)