I know how to solve the system of linear ODEs using Runge Kutta, but very doubtful about the non-linear ones. Can I use the same method as the linear one in solving the non-linear system of ODEs? I am in a doubt regarding the same.
I have solved countless linear and nonlinear ODEs using R-K and have written several books on the subject. My book, Differential Equations, will be free on Saturday (9/10). All of the examples are free on my website. You can even solve ODEs using R-K in an Excel spreadsheet. I have attached 3 examples. I also attached a C code containing a whole list of methods to choose from. http://www.amazon.com/dp/B07DB9J2TK
You can use the Runge Kutta Nystrom method and then the Newton Raphson method for nonlinear differential equations.
First you understand and start from Eulers methods explicitly and implicitly then Rk4 will be easy for understanding. You can also solve system of ode by built-in code of ode in Matlab are Ode45, ode23, for linear and for non-linear differential equations shortly.
These codes basically used the Rk4 method and Rk nystrom method explicitly and implicitly.
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