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Using Runge Kutta method to solve a system of ODEs

hiephoang (3)
Hello everybody
I try to solve a system of ODEs with Visual Studio 2015, and VS shows me result of program but It seems like VS didn't calculate anything.

I think I have problem with 5 functions f1,f2,f3,f4,f5 or arrays, that's why VS can not implement my command. But I don't know where is the mistake. how to fix the program. Thank you in advance! I really appreciate your help.
Below are system of ODEs, result showed in VS and code of program
system of ODEs
f'''+ 3*f*f''-2*f'*f' + q = 0
q''+ 2.25*f*q'= 0
Innitial and boundary conditions: f(0)=f'(0)=1-q(0)=f'(infinity)=q(infinity)=0
Results after debugging:
"Step in the coordinate h=0.25
bb -nan<ind> cc -nan<ind> //-nan<ind> means no number
iter=1 dd= -nan<ind>
x=0 then u= 0
x=0 then y= -nan<ind>
x=0 then z= 7
x=0 then w= -nan<ind>
x=0 then p= -3
x=0.25 then u= -nan<ind>
x=0.25 then y= -nan<ind>
x=0.25 then z= -nan<ind>
x=0.25 then w= -nan<ind>
x=0.25 then p= -nan<ind>
.............................etc``

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#include<math.h>
#include<stdio.h>
#include<conio.h>
#include<iostream>
using namespace std;
double f1(double x, double u, double y, double z, double w, double p)
{
return y;
}
//
double f2(double x, double u, double y, double z, double w, double p)
{
return z;
}
//
double f3(double x, double u, double y, double z, double w, double p)
{
return -3 * u*z + 2 * y*y - w;
}
//
double f4(double x, double u, double y, double z, double w, double p)
{
return p;
}
double f5(double x, double u, double y, double z, double w, double p)
{
return -2.25*u*p;
}    
//
int main(void){
const double EPS = 1e-10;
int i, n = 40;
double h;
    		//
h = 10.0 / n;
//
double *x;
x = new double[n + 1];
x[0] = 0.0;
//
for (i = 0; i<n + 1; i++)
 x[i] = i*h;
 void Outputofarray(double x[], int n);
   {
   printf("\n");
   for (i = 0; i<n + 1; i++)
   {
    cout << x[i] << endl;
   }
    		}
//
cout << "step in the coordinate h= " << h << endl;
    		//
double *u;
u = new double[n + 1];
u[0] = 0.0;
double *y;
y = new double[n + 1];
y[0] = 0.0;
double *z;
z = new double[n + 1];
z[0] = 7.0;
double *w;
w = new double[n + 1];
w[0] = 1.0;
double *p;
p = new double[n + 1];
p[0] = -3.0;
    		//
int iter;
    		//
  double ksi = 0.0, eta = 7.0, gamma = 1.0, epsilon = -3.0;
  double hy, hw, dd, dy, dw;
  double bb, cc, bby, ccy, bbw, ccw;
  double a1, a2, a3, a4;
  double b1, b2, b3, b4;
  double c1, c2, c3, c4;
  double d1, d2, d3, d4;
  double g1, g2, g3, g4;
  iter = 0;
      do
   {
    iter++;
    u[0] = 0.0;
    y[0] = ksi;
    z[0] = eta;
    w[0] = gamma;
    p[0] = epsilon;
//
    for (i = 0; i<n; i++)
    {
    a1 = f1(x[i], u[i], y[i], z[i], w[i], p[i])*h;
    b1 = f2(x[i], u[i], y[i], z[i], w[i], p[i])*h;
    c1 = f3(x[i], u[i], y[i], z[i], w[i], p[i])*h;
    d1 = f4(x[i], u[i], y[i], z[i], w[i], p[i])*h;
    g1 = f5(x[i], u[i], y[i], z[i], w[i], p[i])*h;
    				//
    a2 = f1(x[i] + 0.5*h, u[i] + 0.5*a1, y[i] + 0.5*b1, z[i] + 0.5*c1, w[i] + 0.5*d1, p[i] + 0.5*g1)*h;
    b2 = f2(x[i] + 0.5*h, u[i] + 0.5*a1, y[i] + 0.5*b1, z[i] + 0.5*c1, w[i] + 0.5*d1, p[i] + 0.5*g1)*h;
    c2 = f3(x[i] + 0.5*h, u[i] + 0.5*a1, y[i] + 0.5*b1, z[i] + 0.5*c1, w[i] + 0.5*d1, p[i] + 0.5*g1)*h;
    d2 = f4(x[i] + 0.5*h, u[i] + 0.5*a1, y[i] + 0.5*b1, z[i] + 0.5*c1, w[i] + 0.5*d1, p[i] + 0.5*g1)*h;
    g2 = f5(x[i] + 0.5*h, u[i] + 0.5*a1, y[i] + 0.5*b1, z[i] + 0.5*c1, w[i] + 0.5*d1, p[i] + 0.5*g1)*h;
//
    a3 = f1(x[i] + 0.5*h, u[i] + 0.5*a2, y[i] + 0.5*b2, z[i] + 0.5*c2, w[i] + 0.5*d2, p[i] + 0.5*g2)*h;
    b3 = f2(x[i] + 0.5*h, u[i] + 0.5*a2, y[i] + 0.5*b2, z[i] + 0.5*c2, w[i] + 0.5*d2, p[i] + 0.5*g2)*h;
    c3 = f3(x[i] + 0.5*h, u[i] + 0.5*a2, y[i] + 0.5*b2, z[i] + 0.5*c2, w[i] + 0.5*d2, p[i] + 0.5*g2)*h;
    d3 = f4(x[i] + 0.5*h, u[i] + 0.5*a2, y[i] + 0.5*b2, z[i] + 0.5*c2, w[i] + 0.5*d2, p[i] + 0.5*g2)*h;
    g3 = f5(x[i] + 0.5*h, u[i] + 0.5*a2, y[i] + 0.5*b2, z[i] + 0.5*c2, w[i] + 0.5*d2, p[i] + 0.5*g2)*h;
//

    a4 = f1(x[i] + h, u[i] + a3, y[i] + b3, z[i] + c3, w[i] + d3, p[i] + g3)*h;
    b4 = f2(x[i] + h, u[i] + a3, y[i] + b3, z[i] + c3, w[i] + d3, p[i] + g3)*h;
    c4 = f3(x[i] + h, u[i] + a3, y[i] + b3, z[i] + c3, w[i] + d3, p[i] + g3)*h;
    d4 = f4(x[i] + h, u[i] + a3, y[i] + b3, z[i] + c3, w[i] + d3, p[i] + g3)*h;
    g4 = f5(x[i] + h, u[i] + a3, y[i] + b3, z[i] + c3, w[i] + d3, p[i] + g3)*h;
    
    				//
    u[i + 1] = u[i] + (a1 + 2.0*a2 + 2.0*a3 + a4) / 6.0;
    y[i + 1] = y[i] + (b1 + 2.0*b2 + 2.0*b3 + b4) / 6.0;
    z[i + 1] = z[i] + (c1 + 2.0*c2 + 2.0*c3 + c4) / 6.0;
    w[i + 1] = w[i] + (d1 + 2.0*d2 + 2.0*d3 + d4) / 6.0;
    p[i + 1] = p[i] + (g1 + 2.0*g2 + 2.0*g3 + g4) / 6.0;
    			}
//
    bb = y[n] - 0.0;
    cc = w[n] - 0.0;
    cout << "bb " << bb << " cc " << cc << endl;
    

for (i = 0; i<n + 1; i++)
{
    			cout << "x[i]= " << x[i] << " then u[i]= " << u[i] << endl;
    			cout << "x[i]= " << x[i] << " then y[i]= " << y[i] << endl;
    			cout << "x[i]= " << x[i] << " then z[i]= " << z[i] << endl;
    			cout << "x[i]= " << x[i] << " then w[i]= " << w[i] << endl;
    			cout << "x[i]= " << x[i] << " then p[i]= " << p[i] << endl;
delete[] x;
delete[] u;
delete[] y;
delete[] z;
delete[] w;
delete[] p;
system("pause");
    	}
Last edited on
keskiverto (10402)
Your posted code does not compile. A copy-paste error?
hiephoang (3)
The original code is 316 lines but because of content limit I can only post a half the code. The rest of code is quite similar. It is just iteration of the first part
ne555 (10692)
This is how your code ends 
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		for (i = 0; i < n + 1; i++)
		{
			cout << "x[i]= " << x[i] << " then u[i]= " << u[i] << endl;
			cout << "x[i]= " << x[i] << " then y[i]= " << y[i] << endl;
			cout << "x[i]= " << x[i] << " then z[i]= " << z[i] << endl;
			cout << "x[i]= " << x[i] << " then w[i]= " << w[i] << endl;
			cout << "x[i]= " << x[i] << " then p[i]= " << p[i] << endl;
			delete[] x;
			delete[] u;
			delete[] y;
			delete[] z;
			delete[] w;
			delete[] p;
			system ("pause");
		}
so there you are trying to delete several times the same pointers, and also try to dereference them after being deleted.

Create a small example that reproduces your problem. Simplify the equations to solve.
Also, use meaningful names and comments.
http://www.eelis.net/iso-c++/testcase.xhtml
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