Exactly. So Now You Have the Time Equation, Right?

The idea is for a semi-discrete method. Once you replace the spatial with the matrices, now it all depends on what method do you want to use. Use first order method, second order method, third order method, and that'll all change on what happens to your time. So explicit Euler is RK1, which is like first order, first order difference. And as you go higher, RK2 and RK3, I believe, I don't know if it's as simple as simply central difference because like RK4 gets,. It just gets a little confusing. But if you actually expand them out in terms of, it's actually called Taylor tables