usfkad6_05.cpp

Solutions are obtained for Poissson, diffusion, or wave PDEs homogeneous or nonhomogeneous equations

		if(eqtype[1]==2)  // 2 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y;s)";
				if(eqtype[7]==1)
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\left(\\frac{F_{interior}(x,y;s)+\\Psi(x,y,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(x,y,t=0)}{\\kappa_x^2+\\kappa_y^2+s^2}\\right)";
				else
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\frac{\\Psi(x,y,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(x,y,t=0)}{\\kappa_x^2+\\kappa_y^2+s^2}";
			}
			if(eqtype[2]==1)  // polar coords
			{
				AAA="A(\\kappa_r, \\kappa_{\\theta};s)";
				if(eqtype[7]==1)
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\left(\\frac{F_{interior}(r, \\theta ;s)+\\Psi(r, \\theta,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(r, \\theta,t=0)}{\\kappa_r^2+s^2}\\right)";
				else
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\frac{\\Psi(r, \\theta,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(r, \\theta,t=0)}{\\kappa_r^2+s^2}";
			}
		}
		if(eqtype[1]==3)  // 3 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y, \\kappa_z ;s)";
				if(eqtype[7]==1)
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\left(\\frac{F_{interior}(x,y,z ;s)+\\Psi(x,y,z,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(x,y,z,t=0)}{\\kappa_x^2+\\kappa_y^2+\\kappa_z^2+s^2}\\right)";
				else
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\frac{\\Psi(x,y,z,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(x,y,z,t=0)}{\\kappa_x^2+\\kappa_y^2+\\kappa_z^2+s^2}";
			}
			if(eqtype[2]==1)  // cylindrical coords
			{
				AAA="A(\\kappa_{r:\\theta},\\kappa_{\\theta}, \\kappa_z ;s)";
				if(eqtype[7]==1)
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\left(\\frac{F_{interior}(r, \\theta , z ;s)+\\Psi(r, \\theta , z ,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(r, \\theta , z ,t=0)}{\\kappa_{r:\\theta}^2+\\kappa_z^2+s^2}\\right)";
				else
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\frac{(r, \\theta , z ;s)+\\Psi(r, \\theta , z ,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(r, \\theta , z ,t=0)}{\\kappa_{r:\\theta}^2+\\kappa_z^2+s^2}";
			}
			if(eqtype[2]==2)  // spherical coords
			{
				AAA="A_{\\ell m}(\\kappa_{\\ell: r} ;s)";
				if(eqtype[7]==1)
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\left(\\frac{F_{interior}(\\theta, \\phi, {r};s)+\\Psi(\\theta, \\phi, {r},t=0)+s\\frac{\\partial \\Psi}{\\partial t}(\\theta, \\phi, {r},t=0)}{\\kappa_{\\ell: r}^2+s^2}\\right)";
				else
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\frac{\\Psi(\\theta, \\phi, {r},t=0)+s\\frac{\\partial \\Psi}{\\partial t}(\\theta, \\phi, {r},t=0)}{\\kappa_{\\ell: r}^2+s^2}";

			}
		}
	}
	
	if(eqtype[0]==5)   // frequency domain
	{
		if(eqtype[1]==1)  // 1 dim
		{
			AAA="A(\\kappa_x;\\omega)";
			nonhomf="\\frac{F_{interior}(x;\\omega)}{\\kappa_x^2-\\omega^2}";
		}
		if(eqtype[1]==2)  // 2 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y;\\omega)";
				nonhomf="\\frac{F_{interior}(x,y;\\omega)}{\\kappa_x^2+\\kappa_y^2-\\omega^2}";
			}
			if(eqtype[2]==1)  // polar coords
			{
				AAA="A(\\kappa_r, \\kappa_{\\theta};\\omega)";
				nonhomf="\\frac{F_{interior}(r, \\theta ;\\omega)}{\\kappa_r^2-\\omega^2}";
			}
		}
		if(eqtype[1]==3)  // 3 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y, \\kappa_z ;\\omega)";
				nonhomf="\\\\ \\hspace*{2.6in} \\times  \\frac{F_{interior}(x,y,z ;\\omega)}{\\kappa_x^2+\\kappa_y^2+\\kappa_z^2-\\omega^2}";
			}
			if(eqtype[2]==1)  // cylindrical coords
			{
				AAA="A(\\kappa_{r:\\theta},\\kappa_{\\theta}, \\kappa_z ;\\omega)";
				nonhomf="\\\\ \\hspace*{2.6in} \\times  \\frac{F_{interior}(r, \\theta , z ;\\omega)}{\\kappa_{r:\\theta}^2+\\kappa_z^2-\\omega^2}";
			}
			if(eqtype[2]==2)  // spherical coords
			{
				AAA="A_{\\ell m}(\\kappa_{\\ell: r} ;\\omega)";
				nonhomf="\\frac{F_{interior}(\\theta, \\phi, {r};\\omega)}{\\kappa_{\\ell: r}^2-\\omega^2}";
			}
		}
	}
	
A.nonhomf=nonhomf;
A.AAA=AAA;
return A;
}

// ****************KAPGRTR


pdeans KAPGRTR(pdeans A, int t)
{
std::string  nonhomf, AAA, Nonans1;
if(t==0)   //  diffusion IC
{
			if(eqtype[1]==1)  // 1 dim
		{
			AAA="A(\\kappa_x)";
			nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(x;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "e^{-\\kappa_x^2t}";
		}
		if(eqtype[1]==2)  // 2 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y)";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(x,y;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "e^{-(\\kappa_x^2+\\kappa_y^2)t}";
			}
			if(eqtype[2]==1)  // polar coords
			{
				AAA="A(\\kappa_{\\theta},\\kappa_{r:\\theta})";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(\\theta,r;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "e^{-\\kappa_{r:\\theta}^2t}";
			}
		}
		if(eqtype[1]==3)  // 3 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y, \\kappa_z)";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(x,y,z;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "e^{-(\\kappa_x^2+\\kappa_y^2+\\kappa_z^2)t}";
			}
			if(eqtype[2]==1)  // cylindrical coords
			{
				AAA="A(\\kappa_{r:\\theta},\\kappa_{\\theta}, \\kappa_z)";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(r, \\theta, z;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "\\\\ \\hspace*{3.0in}  e^{-(\\kappa_{r:\\theta}^2+\\kappa_z^2)t}";
			}
			if(eqtype[2]==2)  // spherical coords
			{
				AAA="A_{\\ell m}(\\kappa_{\\ell: r})";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(\\theta,\\phi,{r};0)-\\Psi_{steady \\; state}]";
			Nonans1 = "e^{-\\kappa_{r}^2t}";
			}
		}
		}
		
if(t==1)   //  wave Initial Value
{
			if(eqtype[1]==1)  // 1 dim
		{
			AAA="A(\\kappa_x)";
			nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(x;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "\\cos \\kappa_xt";
		}
		if(eqtype[1]==2)  // 2 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y)";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(x,y;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "\\cos \\sqrt{\\kappa_x^2+\\kappa_y^2}t";
			}
			if(eqtype[2]==1)  // polar coords
			{
				AAA="A(\\kappa_{\\theta},\\kappa_{r:\\theta})";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(\\theta,r;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "\\cos \\kappa_{r:\\theta}t";
			}
		}
		if(eqtype[1]==3)  // 3 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y, \\kappa_z)";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(x,y,z;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "\\cos \\sqrt{\\kappa_x^2+\\kappa_y^2+\\kappa_z^2}t";
			}
			if(eqtype[2]==1)  // cylindrical coords
			{
				AAA="A(\\kappa_{r:\\theta},\\kappa_{\\theta}, \\kappa_z)";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(r, \\theta, z;0)-\\Psi_{steady \\; state}]";
			Nonans1 = "\\\\ \\hspace*{3.0in}  \\cos \\sqrt{\\kappa_{r:\\theta}^2+\\kappa_z^2}t";
			}
			if(eqtype[2]==2)  // spherical coords
			{
				AAA="A_{\\ell m}(\\kappa_{\\ell: r})";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; [\\Psi(\\theta,\\phi,{r};0)-\\Psi_{steady \\; state}]";
			Nonans1 = "\\cos \\kappa_{r}t";
			}
		}
		}
		
if(t==2)   //  wave Initial Velocity
{
			if(eqtype[1]==1)  // 1 dim
		{
			AAA="A(\\kappa_x)";
			nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; \\frac{\\partial \\Psi(x;0)}{\\partial t}";
			Nonans1 = "\\frac{\\sin \\kappa_xt}{\\kappa_x}";
		}
		if(eqtype[1]==2)  // 2 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y)";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; \\frac{\\partial \\Psi(x,y;0)}{\\partial t}";
			Nonans1 = "\\frac{\\sin \\sqrt{\\kappa_x^2+\\kappa_y^2}t}{\\sqrt{\\kappa_x^2+\\kappa_y^2}}";
			}
			if(eqtype[2]==1)  // polar coords
			{
				AAA="A(\\kappa_{\\theta},\\kappa_{r:\\theta})";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; \\frac{\\partial \\Psi(\\theta,r;0)}{\\partial t}";
			Nonans1 = "\\frac{\\sin \\kappa_{r:\\theta}t}{\\kappa_r:\\theta}";
			}
		}
		if(eqtype[1]==3)  // 3 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y, \\kappa_z)";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; \\frac{\\partial \\Psi(x,y,z;0)}{\\partial t}";
			Nonans1 = "\\frac{\\sin \\sqrt{\\kappa_x^2+\\kappa_y^2+\\kappa_z^2}t}{\\sqrt{\\kappa_x^2+\\kappa_y^2+\\kappa_z^2}}";
			}
			if(eqtype[2]==1)  // cylindrical coords
			{
				AAA="A(\\kappa_{r:\\theta},\\kappa_{\\theta}, \\kappa_z)";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; \\frac{\\partial \\Psi(r, \\theta , z;0)}{\\partial t}";
			Nonans1 = "\\\\ \\hspace*{3.0in}  \\frac{\\sin \\sqrt{\\kappa_{r:\\theta}^2+\\kappa_z^2}t}{\\sqrt{\\kappa_{r}^2+\\kappa_z^2}}";
			}
			if(eqtype[2]==2)  // spherical coords
			{
				AAA="A_{\\ell m}(\\kappa_{\\ell: r})";
				nonhomf=" \\\\ \\hspace*{2.6in} \\times \\; \\frac{\\partial \\Psi(\\theta,\\phi,{r};0)}{\\partial t}";
			Nonans1 = "\\frac{\\sin \\kappa_{\\ell: r}t}{\\kappa_{\\ell: r}}";
			}
		}
		}

	
A.nonhomf=nonhomf;
A.AAA=AAA;
A.Nonans1=Nonans1;
return A;
}



pdeans sul(pdeans C, int r)
{
	std::string f, u, U, K;

/*  Global variable formulation  */
std::string ans1, ans2, ans3, ans4, ans5, symb1, symb2;
//sub1, sub2, sub3, sub4, sub5, sy1, sy2;
//	sub1=ans1; 
//	sub2=ans2; 
//	sub3=ans3; 
//	sub4=ans4; 
//	sub5=ans5; 
//	sy1=symb1;
//	sy2=symb2;
	
/* Back to old */

// int r;
// r=0;
f = C.ans1;
u = C.ans2;
U = C.ans3;
// K = C.ans4;

K = C.KAPPA;

int sulmarker;
sulmarker = 0;  //If sulmarker changes to 1, sol'n is in sul; else, in sulsul. 
//  This is done to make the number of options in SUL smaller, so it will compile.


//   CONSTANT COEFFICIENT EQUATION: DIRICHLET CONDITION AT THE LOW END
//                 EIGENFUNCTIONS

//1
if (f=="CCDDHH")
{
ans1 = "\\sin\\kappa_" + u + " " + u + " "; // changed last u
ans2 = " \\kappa_" + u + "=\\frac{\\pi}{" + U + "},\\frac{2\\pi}{" + U +"},\\frac{3\\pi}{"
 + U + "}, \\ldots  ";
ans3 = "\\frac{2}{" + U + "}";
ans4 = "";
ans5 = ans1;
symb1 = "\\sum_{\\kappa_" + u + "}";
symb2 = "\\int_{0}^{" + U + "}\\,d" + u;
sulmarker = 1;
}
 
//2
if (f=="CCDNHH")
{
ans1 = "\\sin \\kappa_" + u + " " + u + " "; // changed last u
ans2 = " \\kappa_" + u + " = \\frac{\\pi}{2" + U + "},\\frac{3\\pi}{2" + U + "},\\frac{5\\pi}{2" + U + "}, \\ldots  ";
ans3 = "\\frac{2}{" + U + "}"; 
ans4 = ""; 
ans5 = ans1;
symb1 = "\\sum_{\\kappa_" + u + "}";
symb2 = "\\int_{0}^{" + U + "}\\,d" + u;
sulmarker = 1;
}

//5
if (f=="CCDRHH")
{
ans1="\\; \\eta_" + u + " (" + u + " ; \\kappa_" + u + ")";
ans2="\\\\  \\eta_" + u + "(" + u + " ; \\kappa_" + u + ") = \\sin \\kappa_" + u + " " + u +
" \\mbox{ where } \\{\\kappa_" + u + "\\} \\mbox{ are the nonzero solutions (maybe imaginary) to  }\\\\ \\alpha_"
 + U + 
" \\sin \\kappa_" + u + U + "  + \\kappa_"+ u + " \\cos  \\kappa_" + u + U + " = 0; \\\\ \\mbox{ also if } \\alpha_" + 
U +  U + " + 1 = 0 \\mbox{ include } \\kappa_" 
+ u + " = 0 , \\eta_" + u + "(" + u + " ; 0) = " + u + ".  \\\\";
ans3="N_{\\kappa_" + u + "}";
ans4=" N_{\\kappa_" + u + "} = \\left\\{ \\begin{array}{ll}\\frac{3}{" + U + "^3}& \\mbox {if } \\kappa_" + u +
 " = 0; \\\\ \\frac{2}{" + U + " + (\\alpha_" + U + " + 1)/(\\alpha_" + U + "{}^2 + \\kappa_" + u + 
 "{}^2)} & \\mbox{ otherwise} . \\end{array} \\right.  "; //new line
ans5 =ans1;
symb1 = "\\sum_{\\kappa_" + u + "}";
symb2 = "\\int_{0}^{" + U + "}\\,d" + u;
sulmarker = 1;
}

//55
if(f=="CCDSHH")
{
ans1 = "\\sin  \\kappa_" + u + " " + u + "";
ans2 = "";
ans3 ="\\frac{2}{\\pi}";
ans4 ="";
ans5 ="\\sin  \\kappa_" + u + " " + u + "";
symb1 ="\\int_{0}^{\\infty} \\,d \\kappa_" + u + "";
symb2="\\int_{0}^{\\infty} \\,d " + u + "";
sulmarker = 1;
}


//   CONSTANT COEFFICIENT EQUATION: DIRICHLET CONDITION AT THE LOW END
//                 NONHOMOGENEOUS FACTORS


//10
if (f=="CCDDHN")
{
ans1="\\eta_" + u + " (" + u + " ; " + K + ")";
ans2=" \\eta_" + u + "(" + u + " ; " + K + ") = \\left\\{ \\begin{array}{ll}" + u + " & \\mbox{ if } "
 + K + " = 0;\\\\ \\sinh " + K + "" + u + " & \\mbox{ otherwise} . \\end{array}\\right.  ";
ans3="M_{" + K + "}";
ans4=" M_{" + K + "} = \\left\\{ \\begin{array}{ll}\\frac{1}{" + U + "} & \\mbox{ if } " + K + 
"= 0, \\\\ \\frac{1}{\\sinh " + K + "" + U + "} & \\mbox{ otherwise} . \\end{array} \\right.  "; 
symb1=""; 
symb2="";
if (eqtype[1] == 1 && (eqtype[0]==1 || eqtype[0]==3))  // 1 dim, time
{ans1="\\frac{x}{X}f_{x=X}";
ans2="";
ans3="";
ans4="";
symb1="";
symb2="";
}
if (eqtype[1] == 1 && eqtype[0]==5)  // 1 dim, freq
{
ans1="\\eta_" + u + " (" + u + " ; " + K + ")";
ans2=" \\eta_" + u + "(" + u + " ; " + K + ") = \\left\\{ \\begin{array}{ll}" + u + " & \\mbox{ if } "
 + K + " = 0;\\\\ \\sin " + K + "" + u + " & \\mbox{ otherwise} . \\end{array}\\right.  ";
ans3="M_{" + K + "}";
ans4=" M_{" + K + "} = \\left\\{ \\begin{array}{ll}\\frac{1}{" + U + "} & \\mbox{ if } " + K + 
"= 0, \\\\ \\frac{1}{\\sin " + K + "" + U + "} & \\mbox{ otherwise} . \\end{array} \\right.  "; 
symb1=""; 
symb2="";
}
sulmarker = 1;
}

//11
if (f=="CCDDNH")
{
ans1="\\; \\eta_" + u + " (" + u + " ; " + K + ")";
ans2=" \\eta_" + u + "(" + u + " ; " + K + ") = \\left\\{ \\begin{array}{ll}" + U + " - "
+ u + " & \\mbox{ if } " + K + " = 0; \\\\ \\sinh " + K + " (" + U + " - " + u + ")& \\mbox{ otherwise} . \\end{array} \\right.  ";
ans3="M_{" + K + "}";
ans4=" M_{" + K + "} = \\left\\{ \\begin{array}{ll}\\frac{1}{" + U + "} & \\mbox{ if } "+ K 
+ " = 0; \\\\ \\frac{1}{\\sinh " + K + "" + U + "} & \\mbox{ otherwise} . \\end{array} \\right.  ";
symb1="";
symb2="";
if (eqtype[1] == 1 && (eqtype[0]==1 || eqtype[0]==3))  // 1 dim, time
{ans1="\\frac{X-x}{X}f_{x=0}";
ans2="";
ans3="";
ans4="";
symb1="";
symb2="";
}
if (eqtype[1] == 1 && eqtype[0]==5)  // 1 dim, freq
{
ans1="\\; \\eta_" + u + " (" + u + " ; " + K + ")";
ans2=" \\eta_" + u + "(" + u + " ; " + K + ") = \\left\\{ \\begin{array}{ll}" + U + " - "
+ u + " & \\mbox{ if } " + K + " = 0; \\\\ \\sin " + K + " (" + U + " - " + u + ")& \\mbox{ otherwise} . \\end{array} \\right.  ";
ans3="M_{" + K + "}";
ans4=" M_{" + K + "} = \\left\\{ \\begin{array}{ll}\\frac{1}{" + U + "} & \\mbox{ if } "+ K 
+ " = 0; \\\\ \\frac{1}{\\sin " + K + "" + U + "} & \\mbox{ otherwise} . \\end{array} \\right.  ";
symb1="";
symb2="";
}
sulmarker = 1;
}

//12
if (f=="CCDNHN")
{
ans1="\\; \\eta_" + u + " (" + u + " ; " + K + ")";
ans2=" \\eta_" + u + "(" + u + " ; " + K + ") = \\left\\{ \\begin{array}{ll}" + u + " & \\mbox{ if } " + K + "= 0, \\\\ \\sinh " + K + " " + u + " &\\mbox{ otherwise} . \\end{array} \\right.  ";
ans3="M_{" + K + "}";
ans4=" M_{" + K+ "} = \\left\\{ \\begin{array}{ll}1 & \\mbox{ if } " + K + "= 0; \\\\ \\frac{1}{" + K + "\\cosh " + K + "" + U + "} & \\mbox{ otherwise} . \\end{array} \\right.  ";
symb1=""; 
symb2=""; 
if (eqtype[1] == 1 && (eqtype[0]==1 || eqtype[0]==3))  // 1 dim, time
{ans1="f_{x=X}x";
ans2="";
ans3="";
ans4="";
symb1="";
symb2="";
}
if (eqtype[1] == 1 && eqtype[0]==5)  // 1 dim, freq
{
ans1="\\; \\eta_" + u + " (" + u + " ; " + K + ")";
ans2=" \\eta_" + u + "(" + u + " ; " + K + ") = \\left\\{ \\begin{array}{ll}" + u + " & \\mbox{ if } " + K + "= 0, \\\\ \\sin " + K + " " + u + " &\\mbox{ otherwise} . \\end{array} \\right.  ";
ans3="M_{" + K + "}";
ans4=" M_{" + K+ "} = \\left\\{ \\begin{array}{ll}1 & \\mbox{ if } " + K + "= 0; \\\\ \\frac{1}{" + K + "\\cos " + K + "" + U + "} & \\mbox{ otherwise} . \\end{array} \\right.  ";
symb1=""; 
symb2=""; 
}
sulmarker = 1;
}


//15 //MAY WANT TO CHANGE THIS TO UNITY
if (f=="CCDNNH")
{
ans1 = "\\cosh " + K + " (" + U + " - " + u + ")";
ans2 = "";
ans3 = "\\frac{1}{\\cosh " + K + " " + U + "}";
ans4 = "";
symb1 = "";
symb2 = "";
if (eqtype[1] == 1 && (eqtype[0]==1 || eqtype[0]==3))  // 1 dim, time
{ans1="f_0";
ans2="";
ans3="";
ans4="";
symb1="";
symb2="";
}
if (eqtype[1] == 1 && eqtype[0]==5)  // 1 dim, freq
{
ans1 = "\\cos " + K + " (" + U + " - " + u + ")";
ans2 = "";
ans3 = "\\frac{1}{\\cos " + K + " " + U + "}";
ans4 = "";
symb1 = "";
symb2 = "";
}
sulmarker = 1;
}

//18
if (f=="CCDRHN")
{
ans1 = "\\eta_" + u + " (" + u + " ; " + K + ")";
ans2 = " \\eta_" + u + "(" + u + " ; " + K + ") = \\left\\{ \\begin{array}{ll}" + u + 
"& \\mbox{ if } " + K + "= 0;\\\\ \\sinh " + K + " " + u + " &\\mbox{ otherwise } . \\end{array} \\right.  ";
ans3 = "M_{" + K + "}";
ans4 = " M_{" + K + "} = \\left\\{ \\begin{array}{ll}\\frac{1}{\\alpha_" + U + " " + U +
" +1} & \\mbox{ if } " + K + " = 0;\\\\ \\frac{1}{\\alpha_" + U + "\\sinh " + K + " "
+ U + " + " + K + " \\cosh " + K + " " + U + "} & \\mbox{ otherwise } . \\end{array} \\right.  ";
symb1 = "";
symb2 = "";