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Would you please check if this code is logically correct?

spring2014 (60)
Dear Friends.
The code below runs for 3 time (for loop). and each time from 5 different files (.txt files) it reads a number (there are 3 different numbers in each file and it should read them one by one in each run and go to other one in other run). and use those numbers to calculate integration of d2x/d2t=t^2 by modified euler methods. while running it works well. But I afraid it be correct by chance and in next step while developing it I realize it.Would you please check from programming point of view it is correct or not?

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  #include <iostream>
#include <cmath>
#include <fstream>


using namespace std;

/* function prototypes */

double f1(double, double, double);
double f2(double, double, double);

double euler2m(double(*)(double, double, double),
               double(*)(double, double, double),
               double, double, double, double,
               double&, double&);

int main()
{
    double ti, xi, vi, tf, xf, vf, dt, tmax;
    int i;


/* initial information */


    /*cout<<"enter the initial value for variable as (ti)"<<endl;
    cin>>ti;
    cout<<"initial value for function x(t) as xi"<<endl;
    cin>>xi;
    cout<<"enter the initial (vi)"<<endl;
    cin>>vi;
    cout<<"enter the step size for integration as dt"<<endl;
    cin>>dt;
    cout<<"enter the tmax to integrate from ti till tmax"<<endl;
    cin>>tmax; */
    ifstream inputFile1("afile-ti.txt");
    ifstream inputFile2("afile-xi.txt");
    ifstream inputFile3("afile-vi.txt");
    ifstream inputFile4("afile-dt.txt");
    ifstream inputFile5("afile-tmax.txt");
    ofstream outputFile("output3.txt");
 /*
    ti = 0.0;             // initial value for variable
    xi = 0.0;             // initial value for function x(t)
    vi = 1.0;             // initial
    dt = 0.1;             // step size for integration
    tmax = 12.0;          // integrate from ti till tmax */

           for (i=0; i<3; i++)
           {
            inputFile1>>tf;
        	inputFile2>>xi;
        	inputFile3>>vi;
        	inputFile4>>dt;
        	inputFile5>>tmax;




/* integration of ODE */
    while (ti <= tmax)
    {
    	tf = ti + dt;
    	euler2m(f1,f2,ti,xi,vi,tf,xf,vf);

        ti = tf;
        xi = xf;
        vi = vf;
    }
    cout<<"t="<<tf<<"\t"<<"x="<<xf<<"\t"<<"x'="<<vf<<"\n";
    outputFile<<"t="<<tf<<"\t"<<"x="<<xf<<"\t"<<"x'="<<vf<<"\n";
           }
    return 0;
}

/*
  Definition of the x'(t) = f1(t,x,x') = x' by the definition
*/
    double f1(double t, double x, double v)
{
    double d1x;
    d1x = v;
    return d1x;
}
/*
 *  Definition of the x"(t) = f2(t,x,x')
*/
    double f2(double t, double x, double v)
{
    double d2x;
    d2x = (t*t);
    return d2x;
}

//-----------------------------------------------------------------------

    double euler2m(double(*d1x)(double, double, double),
                   double(*d2x)(double, double, double),
                   double ti, double xi, double vi, double tf,
                   double& xf, double& vf)
    {
        xf = xi + d1x(ti,xi,vi)*(tf-ti);
        vf = vi + d2x(ti,xi,vi)*(tf-ti);
    /* correction */
        xf = xi + (d1x(ti,xi,vi)+d1x(ti,xf,vf))*0.5*(tf-ti);
        vf = vi + (d2x(ti,xi,vi)+d2x(ti,xf,vf))*0.5*(tf-ti);
       return 0.0;
    }
dhayden (5798)
You aren't initializing ti. Should line 53 be inputFile1>>ti?
spring2014 (60)
Yes. Thanks for your comment. But except that is this code well written or it could be written in better way?
dhayden (5798)
Sorry, it wasn't clear that you were looking for more general comments. I think the code is good overall. Here are some minor points.
- Names like inputFile1, inputFile2 etc. aren't very descriptive. Since they contain specific values, maybe call them tiFile, xiFile etc.
- Magic Constants" like the names of the input files should be defined at the top of the source file. That way it's easy to find them if they need to change.
- Use consistent indentation. main(), f1(), f2() and euler2m() are all indented inconsistently.
- You need more comments. At the beginning, give a brief description of what it does. If it's an assignment, mention where you can find the assignment. I look at euler2m() and see a magic formula of some sort. What is it? You don't need a lot, even a search term for the internet will do.
- If euler2m() always returns 0.0, then why return a value at all? Why not make it void?
- The comments between lines 45 and 49 should go with the declarations of the variables (line 20). You'll want to split up the declarations into multiple lines.

spring2014 (60)
Thanks a lot. I applied your comments.
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