I'm trying to write a java programme that will solve the system of ordinary differential equations using the Runge-Kutta fourth-order (RK4) technique. I need to solve a system of five equations. Those are not linear.
And determining all of the equilibrium solutions to this system of differential equations also requires.
Can someone help me? Thank you in advance.
I have solved may equations of this type. It is a relatively simple process that I explain in detail in my book, Differential Equations, which is free today (12/2). There are many examples included which are all free at the link listed at the beginning. While you might accomplish this using Java, I would never recommend anyone ever using Java for anything. The best programming language to use for such a task is C. If you don't have a C compiler, you can get Digital Mars for free. Here is a link to the free book https://read.amazon.com/kp/embed?asin=B07DB9J2TK&preview=newtab&linkCode=kpe&ref_=cm_sw_r_kb_dp_9FDBP0M6R3HVKDWY7M18
The ebook is only $0.99 every day. Differential Equations will be free again on this Saturday, 12/10. Post the equations and I will set it up for you.
This set of ODEs can easily be solved using the Forward Euler Method, as implemented in the attached spreadsheet. If you use small time steps this will be adequate. A more advanced method like 4th Order Runge-Kutta would allow you to use larger time steps. I have many RK4 examples. This should get you started. You must have some values of the 14 constants before proceeding.
Thank you very much. It is very helpful. If you have implemented a java file, it would be really nice. I am struggling with my java code to illustrate the results.
I would never recommend anyone use java for anything. If you need to write code, do it in C. In the attached zip file you will find the code (ode.c) to solve this ODE using Forward Euler and also 4th Order Runge-Kutta. The output of the code (ode.txt) lists the results, which are close but not exactly the same. This is why we must sometimes use higher order methods.
Hereby attached is a system of three Ordinary Differential Equations (ODE). We have to use numerical methods such as RK4 and Euler to obtain the results using Java. I think RK4 is better for this kind of problem. In this thread, Dudley J Benton has already mentioned C programming for this. It is really amazing.
For the parameter values, you can use your own values for your convenience.
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