As I understand it, RK methods are based on integrating a polynomial spline. I'm unsure if I can use them for the Schrödinger wave equation as I can't think of what it would mean to interpolate across a complex domain. I know it's not right to say $C=R^2$ but either way I still don't understand how one would interpolate over R^2 into R^2. Beyond asking if the method is valid, I'd like to know what other questions I should be asking about interpolation overall.
2026-03-26 17:43:18.1774546998
Runge-Kutta methods for complex valued differential equations
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The Runge-Kutta formulas for a complex-valued function are exactly the same as for a real-valued function. It's just that you do the arithmetic with complex numbers. The independent variable, however, is still real.