why is this code showing segmentation fault(core dumped)?

 #include<iostream>
using namespace std;
class wave
{
public:
  void initialdata(double **,int ,int);
  void solveFD(double **,double *,double *,double ,double ,double,int,int );
};
void wave::initialdata(double **u,int nx,int nt)
{
  int i,j;
  for (j=1;j<nt;j++)
    for (i=1;i<nx;i++)
    {
      if(i<=20) 
      {
        u[i][j]=2.0;
      }
      else {u[i][j]=1.0;}
   }
}
//
void wave::solveFD(double **u,double *x,double *t,double  c,double dt,double dx,int nx,int nt)
{
  int i,j;
  for(j=1;j<nt;j++)
    for (i=1;i<nx;i++)
    {
      x[i]=(i-1)*dx;
      t[j]=(j-1)*dt;
      u[i][j+1]=u[i][j]-(c*dt/dx)*(u[i+1][j]-u[i][j]);
    }
}
//
int main()
{
  int i,j;
  int numx=101,numt=101;
  double  cvalue=1.0;
  double **umatrix,*xmatrix,*tmatrix,dtval,dxval;
  dtval=1.0/(numt-1);
  dxval=1.0/(numx-1);
  umatrix=new double *[numx+1];
  xmatrix=new double [numx+1];
  tmatrix=new double [numt+1];
  for (i=1;i<numt;i++)
  {
    umatrix[i]=new double [numt+1];
  }
  wave wave1;
  wave1.initialdata(umatrix,numx,numt);
  wave1.solveFD(umatrix,xmatrix,tmatrix,cvalue,dtval,dxval,numx,numt);
  for (j=1;j<numt;j++)
    for (i=1;i<numx;i++)
    {
      cout<<umatrix[i][j];
    }
  for (i=1;i<numt;i++)
  {
    delete umatrix[i];
  }
  delete umatrix,xmatrix,tmatrix;
  return 0;
}