Smarty Pixels does numerical Ordinary Differential Equation (ODE) and Differential Algebraic Equation (DAE) solving. If your application involves ODE and DAE solving, we hope you’ll consider our software. Our scientific software performs very well on medium sized applications, even very difficult problems.

Our recent journal artical [EN2020] developes and implements a validated and non-validated defect Taylor series method for solving ODE. The stepsize is “just” within the radius of convergence of the Taylor series solution, and it performs well. This paper extends the thesis results in [E2017], where is was realized that stepsize selection in the rigorous defect control of Taylor series methods was a concern and a difficult problem to resolve.

Graph of typical Taylor and Hermite defect.

Publications

EN2020

Ernsthausen J.M. and Nedialkov N.S.: Stepsize selection in the rigorous defect control of Taylor series methods. Journal of Computational and Applied Mathematics, 368, (2020). [link].

EN2017

Ernsthausen J.M.: Rigorous defect control and the numerical solution of ordinary differential equations. MSc, McMaster University, Hamilton (2017). [link].