Advanced Proof of 4th Order Runge-Kutta Method

Hello,

i'm a math student and i do need help about the proof of Runge Kutta Method of 4th order. Especially i need information about how to find the terms k_{1}, k_{2}, k_{3}, k_{4.} There has to be explanations in the proof about four of them, step by step. Otherwise it is not useful for me :(. Wherever i check, there is such a note like "it is beyond us to show how these terms can be found but we'll explain a little bit". However this is not enough for me. Is there anyone who can help me about finding an advanced proof of 4th order Runge-Kutta?

Re: Advanced Proof of 4th Order Runge-Kutta Method

Re: Advanced Proof of 4th Order Runge-Kutta Method

i guess i couln't explain myself. i looked at there already but there is no information about how i can obtain the term k1, k2, k3 and k4. i don't need the formulas, there are dozens of them but need the instructions about how i can obtain the terms k1, k2, k3 and k4 en detail. But thanks anyway :)