7.1.6-ODEs: Second-Order Runge-Kutta

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These videos were created to accompany a university course, Numerical Methods for Engineers, taught Spring 2013. The text used in the course was "Numerical Methods for Engineers, 6th ed." by Steven Chapra and Raymond Canale.
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Hi. Mr. Jacob Bishop. I have one doubt to ask you. Is there any chance of solving ODE by Runge-Kutta second order with an additional K? For example K3= hf(yn+C0K1) where K1=hf(yn); K2=hf(yn+C1K0). Please consider C1, C0 are constants like q11 etc.
Thanks.

freshipalir
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Need page 7.29 to understand better, where these methods get their coefficient from. I hope you will answer and send me a link.
Thx

nunziorusso
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I don't get it, how can you use different values to solve the same equation? There has to be one more accurate than the others, right? I mean, the way I see it is I can take a random value for a and call it "the random method"

carlos
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Great video but I wish more videos would give an example. Numbers and symbols are not good enough sometimes.

jer
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how can i make FORTRAN -77 program on Runge Kutta 4th order method for ODE2?

romygupta
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It was very useful, thank you! saludos de México

hugot
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The vids are helpful but please try to use examples

lukheleteboho