Watch Your Step: Integrating Nonlinear Dynamical Flows by Stepping Through Space and Time
Nonlinear dynamical flows are often solved approximately by numerical integration based on advancing the independent variable, typically time. Here, we present a unified framework for numerical integration of differential equations based on advancing either the dependent variable, often space, or the independent variable, or any combination of the two. Spacetime stepping unifies and extends previous work. In particular, dependent variable stepping can produce better numerical results and also more faithfully describe the underlying physics, thereby providing both practical and conceptual benefits. We indicate extensions to higher dimensions.
Nonlinear flows, numerical integration, spacetime, time, arc length
Kia, Behnam; Lindner, John F.; and Ditto, William L., "Watch Your Step: Integrating Nonlinear Dynamical Flows by Stepping Through Space and Time" (2014). International Journal of Bifurcation and Chaos, 24(11), 1450145-. 10.1142/S0218127414501454. Retrieved from https://openworks.wooster.edu/facpub/206