//		-*- Mode: Java -*-
// Author(s):	J. Robert Buchanan and Zhoude Shao
// Address:	Department of Mathematics
//		Millersville University
//      	P.O. Box 1002
//		Millersville, PA 17551-0302
// Phone:	717-871-7305
// FAX:		717-871-7948
// Email:	Robert.Buchanan@millersville.edu, Zhoude.Shao@millersville.edu
//
// Date:	01/31/2017
//
// Purpose:	Crank-Nicolson implicit finite difference method for solving
//		the homogeneous heat equation with Dirichlet boundary
//		conditions.
//
// To compile:	javac cranknicolsonheat.java
// To execute:	java cranknicolsonheat
//
import java.io.*;

public class cranknicolsonheat
{

    public static double initcond(double x)
    {
	return(100.0)	;
    }	// end of function initcond( )

    // Crout factorization for solving a tridiagonal system of equations
    public static void crout(
			     int nrows	,	// dimension of system
			     double [][] a,	// tridiagonal linear system
			     double [] x	// solution of system
			     )
    {
	int i;	// counter(s)
	double l[][] = new double[nrows][];	// lower triangular matrix
	double u[][] = new double[nrows][];	// upper triangular matrix
	double z[] = new double[nrows];
	for ( i=0 ; i<nrows ; i++ ) {
	    l[i] = new double[2];
	    u[i] = new double[2];
	}	// end of for ( i ) loop
	l[0][0] = a[0][0];
	u[0][1] = a[0][1]/l[0][0];
	z[0] = a[0][3]/l[0][0];
	for ( i=1 ; i<nrows-1 ; i++ ) {
	    l[i][0] = a[i][0];
	    l[i][1] = a[i][1]-l[i][0]*u[i-1][1];
	    u[i][1] = a[i][2]/l[i][1];
	    z[i] = (a[i][3]-l[i][0]*z[i-1])/l[i][1];
	}	// end of for ( i ) loop
	l[nrows-1][0] = a[nrows-1][1];
	l[nrows-1][1] = a[nrows-1][2]-l[nrows-1][0]*u[nrows-2][1];
	z[nrows-1] = (a[nrows-1][3]-l[nrows-1][0]*z[nrows-2])/l[nrows-1][1];
	x[nrows-1] = z[nrows-1];
	for ( i=nrows-2 ; i>-1 ; i-- ) {
	    x[i] = z[i]-u[i][1]*x[i+1];
	}	// end of for ( i ) loop
	return	;
    }	// end of function crout( )
    
    public static void main(String args[])
    {
	int i, j;	// counter(s)
	int nrows = 10-1;
	double h;	// spatial discretization step size
	double k;	// temporal discretization step size
	double r;	// method parameter
	double a[][] = new double[nrows][];	// augmented tridiagonal matrix
	double soln[] = new double[nrows];	// result for new time

	// Set step sizes
	h = 1.0/((double)(nrows+1))	;
	k = 0.004	;
	r = k/(h*h)	;
	// Set initial conditions and populate augmented tridiagonal matrix
	for ( j=0 ; j<nrows ; j++ ) soln[j]=initcond(((double)(j+1))*h);
	// First row of matrix
	a[0] = new double[4];
	a[0][0] = 2.0*(1.0+r);
	a[0][1] = -r;
	a[0][2] = 0.0;
	// Rows 2 through nrows-1 of matrix
	for ( i=1 ; i<(nrows-1) ; i++ ) {
	    a[i] = new double[4];
	    a[i][0] = -r;
	    a[i][1] = 2.0*(1+r);
	    a[i][2] = -r;
	}	// end of for ( i ) loop
	// Last row of matrix
	a[nrows-1] = new double[4];
	a[nrows-1][0] = 0.0;
	a[nrows-1][1] = -r;
	a[nrows-1][2] = 2.0*(1.0+r);
	// Iterate for t = 0, k, 2k, ..., 15k
	for ( j=0 ; j<15+1 ; j++ ) {
	    System.out.printf("%8.4f ",0.0);
	    System.out.printf("%8.4f ",soln[0]);
	    a[0][3] = 2.0*(1.0-r)*soln[0];
	    a[0][3]+= r*soln[1];
	    for ( i=1 ; i<nrows-1 ; i++ ) {
		System.out.printf("%8.4f ",soln[i])	;
		a[i][3] = r*soln[i-1];
		a[i][3]+= 2.0*(1-r)*soln[i];
		a[i][3]+= r*soln[i+1];
	    }	// end of for ( i ) loop
	    System.out.printf("%8.4f ",soln[nrows-1]);
	    a[nrows-1][3] = r*soln[nrows-2];
	    a[nrows-1][3]+= 2.0*(1.0-r)*soln[nrows-1];
	    System.out.printf("%8.4f\n",0.0)	;
	    crout(nrows,a,soln);
	}	// end of for ( j ) loop
    }	// end of function main( )
}

//
//	EOF
//