Yep! Optimize (solve in infinite dimensions) and then discretize onto a finite basis has typically led to much better and stable methods than a discretize and then optimize approach.
Time-scale calculus is a pretty niche theoretical field that looks at blending the analysis of difference and differential equations, but I'm not aware of any algorithmic advances based on it.
Time-scale calculus is a pretty niche theoretical field that looks at blending the analysis of difference and differential equations, but I'm not aware of any algorithmic advances based on it.