Hey Guys. This is my first major program and I thought it would be helpful for someone to share here. From what research I could gather, there is no 4th order differential equation solver for the TI-84 Plus CE.

A quick run through of how it works/ how to run and use the program.
1. User determines the set of first order differential equations corresponding to the given differential equation.
ex: y''+ y' + 3y + x = 5 => y' = Q(x); Q'(x) = -Q(x) - 3y - x +5
2. User writes the functions in the function editor (y= button) in order using PQRSTUVWYZ. P corresponds with y, Q corresponds with y', etc. (As there are only 10 y vars, the program can only handle up to 10th order differential equations). X input remains the same as usual.
(You may want to disable output of each function for easier reading of the graph later)
Write in the form of "y(n) = (dy(n)/dx)." For example, for y' = Q(x), input y1 = Q.
For Q'(x) = -Q(x) - 3y - x +5, input y2 = -Q - 3P - X + 5.
3. Run the program
4. Set number of function outputs to the number of functions you wrote in step 2
5. Input the span of the approximation. This is the minimum and maximum x value that the ODE will be approximated at, ex: {0,10}
6. Input initial values. Ex: Write y(0) = 0, y'(0) = 3 as {0,3}
7. Input change in x. How small this is will increase accuracy of the approximation.
8. The function will run for a while depending on the size of the span and the smallness of the change in x. This is an issue I've tried to work on, but this may just be due to the limitations of the ti-84. If you look at the code and see something causing a large performance drop, PLEASE let me know.
9. The function will store the y values for each x values in the lists FN1 -> FN10 and will store the x values in XVALS. It also shows these values in a scatter plot. Just hit the Graph button.

My next goal is to use the outputs of this program to program the shooting method for boundary value problems. However, the program already completes very slowly and using the shooting method will heavily increase execution time. If somebody would like to take a look at the code to see if there is a way to speed up the process, I would be very grateful.

https://github.com/Nogdoesrandomstuff/Ordinary-Differential-Equation-Solver-TI-84-Plus-CE
  
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