usfkad6_05.cpp

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

				AAA="A(s;\\kappa_{\\theta}, \\,\\kappa_{r : \\theta})";
				nonhomf="F_{z=" + BC + "}(s;r, \\theta)";
				}
			}
				if(r==3)  // theta
			{
				KAPPA="\\sqrt{\\kappa_{r:z}^2+s}";
				AAA = "A(s;\\kappa_z,\\kappa_{r:z})";
				nonhomf="F_{\\theta=" + BC + "}(s;z,r)";
			}
			if(r==5)  // rho
			{
				KAPPA="\\sqrt{\\kappa_z^2+s}";
				AAA = "A(s; \\kappa_{\\theta}, \\kappa_z)";
				nonhomf="F_{r=" + BC + "}(s; z, \\theta)";
			}
			if(r==6)   // r 3-D
			{
				KAPPA="\\sqrt{-s}";
				AAA = "A(s)";
				nonhomf="F_{r=" + BC + "}(s; \\theta, \\phi)";
			}
		}
	}
	if(eqtype[0]==3)    // wave, time
	{
		if(eqtype[1]==2)  // 2-D (1-D is special)
		{
			if(r==0)  //x
			{
				KAPPA = "\\kappa_y";
				AAA="A(\\kappa_y)";
				nonhomf="f_{x=" + BC + "}(y)";
			}
			if(r==1)  // y
			{
				KAPPA = "\\kappa_x";
				AAA="A(\\kappa_x)";
				nonhomf="f_{y=" + BC + "}(x)";
			}
			if(r==3)  // theta
			{
				KAPPA = "\\kappa_{r}";
				AAA="A(\\kappa_{r})";
				nonhomf="f_{\\theta=" + BC + "}(r)";
			}
			if(r==4)   // r 2-D
			{
				KAPPA = "\\kappa_{\\theta}";
				AAA="A(\\kappa_{\\theta})";
				nonhomf="f_{r=" + BC + "}(\\theta)";
			}
		}
		if(eqtype[1]==3)   // 3-D
		{
			if(r==0)   // x
			{
				KAPPA="\\sqrt{\\kappa_y^2+\\kappa_z^2}";
				AAA="A(\\kappa_y, \\, \\kappa_z)";
				nonhomf="f_{x=" + BC + "}(y,z)";
			}
			if(r==1)   // y
			{
				KAPPA="\\sqrt{\\kappa_x^2+\\kappa_z^2}";
				AAA="A(\\kappa_x, \\, \\kappa_z)";
				nonhomf="f_{y=" + BC + "}(x,z)";
			}
			if(r==2)  // z
			{
				if(eqtype[2]==0)   // rect
				{
					KAPPA="\\sqrt{\\kappa_x^2+\\kappa_y^2}";
					AAA="A(\\kappa_x, \\, \\kappa_y)";
					nonhomf="f_{z=" + BC + "}(x,y)";
				}
				if(eqtype[2]==1)  // cyl
				{
					KAPPA="\\kappa_{r:\\theta}";
					AAA = "A(\\kappa_{\\theta},\\kappa_{r:\\theta})";
					nonhomf="f_{z=" + BC + "}(\\theta,r)";
				}
			}

			if(r==3)   // theta
			{
				KAPPA="\\kappa_{r:z}";
				AAA = "A(\\kappa_z,\\kappa_{r:z})";
				nonhomf="f_{\\theta=" + BC + "}(z,r)";
			}
			if(r==5)  // rho
			{
				KAPPA="\\kappa_z";
				AAA = "A(\\kappa_{\\theta},\\kappa_z)";
				nonhomf="f_{r=" + BC + "}(\\theta, z)";
			}
			if(r==6)  // r 3-D
			{
				AAA="A_{\\ell m}";
				nonhomf="f_{r=" + BC + "}(\\theta,\\phi)";
			}
		}
	}
	if(eqtype[0]==4)   // wave, s plane
	{
		if(eqtype[1]==1)    // 1-D
		{
			KAPPA=" s";
			AAA="A(s)";
			nonhomf="F_{x=" + BC + "}(s)";
		}
		if(eqtype[1]==2)  // 2-D
		{
			if(r==0)  // x
			{
				KAPPA="\\sqrt{\\kappa_y^2+s^2}";
				AAA="A(s;\\kappa_y)";
				nonhomf="F_{x=" + BC + "}(s;y)";
			}
			if(r==1)  // y
			{
				KAPPA="\\sqrt{\\kappa_x^2+s^2}";
				AAA="A(s;\\kappa_x)";
				nonhomf="F_{y=" + BC + "}(s;)";
			}
			if(r==3)  // theta   
			{
				KAPPA = "\\sqrt{\\kappa_r^2+s^2}";
				AAA="A(s;\\kappa_r)";
				nonhomf="f_{\\theta=" + BC + "}(s;r)";
			}
			if(r==4)  // r 2-D   
			{
				KAPPA = "s";
				AAA="A(s;\\kappa_{\\theta})";
				nonhomf="f_{r=" + BC + "}(s;\\theta)";
			}  //**************???????????????
		}
		if(eqtype[1]==3)   // 3-D
		{
			if(r==0)   // x
			{
				KAPPA="\\sqrt{\\kappa_y^2+\\kappa_z^2+s^2}";
				AAA="A(s;\\kappa_y,\\kappa_z)";
				nonhomf="F_{x=" + BC + "}(s;y,z)";
			}
			if(r==1)  // y
			{
				KAPPA="\\sqrt{\\kappa_x^2+\\kappa_z^2+s^2}";
				AAA="A(s;\\kappa_x,\\kappa_z)";
				nonhomf="F_{y=" + BC + "}(s;x,z)";
			}
			if(r==2)  // z
			{
			if(eqtype[2]==0)   // rect
				{
				KAPPA="\\sqrt{\\kappa_x^2+\\kappa_y^2+s^2}";
				AAA="A(s;\\kappa_x,\\kappa_y)";
				nonhomf="F_{z=" + BC + "}(s;x,y)";
				}
				if(eqtype[2]==1)  // cyl
				{
				KAPPA="\\sqrt{\\kappa_{r:\\theta}^2+s^2}";
				AAA = "A(s;\\kappa_{\\theta},\\kappa_{r:\\theta})";
				nonhomf="F_{z=" + BC + "}(s;\\theta,r)";
				}
			}
				if(r==3)  // theta
			{
				KAPPA="\\sqrt{\\kappa_{r:z}^2+s^2}";
				AAA = "A(s;\\kappa_z,\\kappa_{r:z})";
				nonhomf="F_{\\theta=" + BC + "}(s;z,r)";
			}
			//if(r==5)  // rho
			//{
			//	KAPPA="\\sqrt{\\kappa_z^2+s}";
			//	AAA = "A(s; \\kappa_{\\theta}, \\kappa_z)";
			//	nonhomf="F_{r=" + BC + "}(s; z, \\theta)";
			//}
			if(r==5)   // rho
			{
				KAPPA="\\sqrt{\\kappa_z^2+s^2}";
				AAA="A(s; \\kappa_{\\theta}, \\kappa_z)";
				nonhomf="F_{r=" + BC + "}(s; \\theta, z)";
			}
			if(r==6)
			{
				KAPPA="is";
				AAA="A(s; \\ell, m)";
				nonhomf="F_{r=" + BC + "}(s; \\theta, z)";
			}
		}
	}
	if(eqtype[0]==5)   //  wave, frequency
	{
		if(eqtype[1]==1)   // 1-D
		{
			KAPPA=" \\omega ";
/*				if (mtrx[r][5]=="O")
				{
					KAPPA=" \\omega";
				}
				if (mtrx[r][5]=="I")
				{
					KAPPA=" \\omega";
				}
*/
			AAA="A(\\omega)";
			nonhomf="F_{x=" + BC +"}(\\omega)";
		}
		if(eqtype[1]==2)   // 2-D
		{
			if(r==0)  // x
			{
				KAPPA="\\sqrt{\\kappa_y^2-\\omega^2}";
				if (mtrx[r][5]=="O")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_y^2}";
				}
				if (mtrx[r][5]=="I")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_y^2}";
				}
				AAA="A(\\omega,\\kappa_y)";
				nonhomf="F_{x=" + BC +"}(\\omega,y)";
			}
			if(r==1)  // y
			{
				KAPPA="\\sqrt{\\kappa_x^2-\\omega^2}";
				if (mtrx[r][5]=="O")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_x^2}";
				}
				if (mtrx[r][5]=="I")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_x^2}";
				}
				AAA="A(\\omega,\\kappa_x)";
				nonhomf="F_{y=" + BC +"}(\\omega,x)";
			}
			if(r==3)  // theta   
			{
				KAPPA = "\\sqrt{\\kappa_r^2-\\omega^2}";
				AAA="A(\\omega; \\kappa_r)";
				nonhomf="f_{\\theta=" + BC + "}(\\omega;r)";
			}
			if(r==4)  // r 2-D   
			{
				KAPPA = "i \\omega";
				AAA="A(\\omega;\\kappa_{\\theta})";
				nonhomf="f_{r=" + BC + "}(\\omega;\\theta)";
			}  //**************???????????????
		}
		if(eqtype[1]==3)   //   3-D
		{
			if(r==0)   // x
			{
				KAPPA="\\sqrt{\\kappa_y^2+\\kappa_z^2-\\omega^2}";
				if (mtrx[r][5]=="O")
				{
					KAPPA="\\sqrt{\\omega^2-\\kappa_y^2-\\kappa_z^2}";
				}
				if (mtrx[r][5]=="I")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_y^2-\\kappa_z^2}";
				}
				AAA="A(\\omega;\\kappa_y,\\kappa_z)";
				nonhomf="F_{x=" + BC+ "}(\\omega;y,z)";
			}
			if(r==1)  // y
			{
				KAPPA="\\sqrt{\\kappa_x^2+\\kappa_z^2-\\omega^2}";
				if (mtrx[r][5]=="O")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_x^2-\\kappa_z^2}";
				}
				if (mtrx[r][5]=="I")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_x^2-\\kappa_z^2}";
				}
				AAA="A(\\omega;\\kappa_x,\\kappa_z)";
				nonhomf="F_{y=" + BC+ "}(\\omega;x,z)";
			}
			if(r==2)  // z
			{
			if(eqtype[2]==0)   // rect
				{
				KAPPA="\\sqrt{\\kappa_x^2+\\kappa_y^2-\\omega^2}";
				if (mtrx[r][5]=="O")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_x^2-\\kappa_y^2}";
				}
				if (mtrx[r][5]=="I")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_x^2-\\kappa_y^2}";
				}
				AAA="A(\\omega;\\kappa_x,\\kappa_y)";
				nonhomf="F_{z=" + BC+ "}(\\omega;x,y)";
				}
				if(eqtype[2]==1)  // cyl
				{
				KAPPA="\\sqrt{\\kappa_{r:\\theta}^2- \\omega^2}";
				if (mtrx[r][5]=="O")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_{r:\\theta}^2}";
				}
				if (mtrx[r][5]=="I")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_{r:\\theta}^2}";
				}
				AAA = "A(\\omega;\\kappa_{\\theta},\\kappa_{r:\\theta})";
				nonhomf="F_{z=" + BC + "}(\\omega;\\theta,r)";
				}
			}
			if(r==3)  // theta
			{
				KAPPA="\\sqrt{\\kappa_{r:z}^2-\\omega^2}";
				AAA = "A(\\omega;\\kappa_z,\\kappa_{r:z})";
				nonhomf="F_{\\theta=" + BC + "}(\\omega;z,r)";
			}
			if(r==5)  // rho
			{
				KAPPA="\\sqrt{\\kappa_z^2-\\omega^2}";
				AAA = "A(\\omega; \\kappa_{\\theta}, \\kappa_z)";
				nonhomf="F_{r=" + BC + "}(\\omega; z, \\theta)";
			}
				if(r==5)  // rho
			{
				KAPPA="\\sqrt{\\kappa_z^2-\\omega^2}";
				if (mtrx[r][5]=="O")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_z^2}";
				}
				if (mtrx[r][5]=="I")
				{
					KAPPA=" \\sqrt{\\omega^2-\\kappa_z^2}";
				}
				AAA = "A(\\omega;\\kappa_{\\theta},\\kappa_z)";
				nonhomf="F_{r=" + BC + "}(\\omega;\\theta,z)";
			}
			if(r==6)   // r 3-D
			{
				KAPPA="\\omega";
/*				if (mtrx[r][5]=="O")
				{
					KAPPA=" \\omega";
				}
				if (mtrx[r][5]=="I")
				{
					KAPPA="\\omega";
				}			
*/
				AAA = "A(\\omega;\\ell, m)";
				nonhomf="F_{r=" + BC + "}(\\omega;\\theta,\\phi)";
				}
		}
	}
C.KAPPA=KAPPA;
C.nonhomf=nonhomf;
C.AAA=AAA;
return C;
}
 
// ************* KAPPAGR ********


pdeans KAPPAGR(pdeans A)
//  Puts the coeff in AAA, and the nohomog function in nonhomf or the Green's term

{
	std::string nonhomf, AAA;

	if(eqtype[0]==0 || eqtype[0]==1 || eqtype[0]==3)   // time domain
	{
		if(eqtype[1]==1)  // 1 dim
		{
			AAA="A(\\kappa_x)";
			nonhomf="\\frac{f_{interior}(x)}{\\kappa_x^2}";
		}
		if(eqtype[1]==2)  // 2 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y)";
				nonhomf="\\frac{f_{interior}(x,y)}{\\kappa_x^2+\\kappa_y^2}";
			}
			if(eqtype[2]==1)  // polar coords
			{
				AAA="A(\\kappa_r, \\kappa_{\\theta})";
				nonhomf="\\frac{f_{interior}(r, \\theta)}{\\kappa_r^2}";
			}
		}
		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{f_{interior}(x,y,z)}{\\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{f_{interior}(r, \\theta , z)}{\\kappa_{r:\\theta}^2+\\kappa_z^2}";
			}
			if(eqtype[2]==2)  // spherical coords
			{
				AAA="A_{\\ell m}(\\kappa_{\\ell: r})";
				nonhomf="\\frac{f_{interior}(\\theta, \\phi, {r})}{\\kappa_{\\ell: r}^2}";
			}
		}
	}
	
	if(eqtype[0]==2)   // s-plane diffusion 
	{
		if(eqtype[1]==1)  // 1 dim
		{
			AAA="A(\\kappa_x;s)";
			if(eqtype[7]==0)
				nonhomf="\\frac{\\Psi(x,t=0)}{\\kappa_x^2+s}";
			else 
				nonhomf="\\left(\\frac{F_{interior}(x;s)+\\Psi(x,t=0)}{\\kappa_x^2+s}\\right)";
		}
		if(eqtype[1]==2)  // 2 dim
		{
			if(eqtype[2]==0)  // Rect coords
			{
				AAA="A(\\kappa_x,\\kappa_y;s)";
			if(eqtype[7]==1)
				nonhomf="\\left(\\frac{F_{interior}(x,y;s)+\\Psi(x,y,t=0)}{\\kappa_x^2+\\kappa_y^2+s}\\right)";
			else
				nonhomf="\\frac{\\Psi(x,y,t=0)}{\\kappa_x^2+\\kappa_y^2+s}";


			}
			if(eqtype[2]==1)  // polar coords
			{
				AAA="A(\\kappa_r, \\kappa_{\\theta};s)";
			if(eqtype[7]==1)
				nonhomf="\\left(\\frac{F_{interior}(r, \\theta;s)+\\Psi(r, \\theta, t=0)}{\\kappa_r^2+s}\\right)";
			else
				nonhomf="\\frac{\\Psi(r, \\theta,t=0)}{\\kappa_r^2+s}\\right)";

			}
		}
		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)}{\\kappa_x^2+\\kappa_y^2+\\kappa_z^2+s}\\right)";
				else
					nonhomf="\\\\ \\hspace*{2.6in} \\times \\frac{\\Psi(x,y,z,t=0)}{\\kappa_x^2+\\kappa_y^2+\\kappa_z^2+s}";

			}
			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)}{\\kappa_{r:\\theta}^2+\\kappa_z^2+s}\\right)";
				else
					nonhomf="\\\\ \\hspace*{2.6in} \\times  \\frac{\\Psi(r, \\theta , z ,t=0)}{\\kappa_{r:\\theta}^2+\\kappa_z^2+s}";

			}
			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)}{\\kappa_{\\ell: r}^2+s}\\right)";
				else
					nonhomf="\\frac{\\Psi(\\theta, \\phi, {r},t=0)}{\\kappa_{\\ell: r}^2+s}";
			}
		}
	}
	if(eqtype[0]==4)   // s-plane wave 
	{
		if(eqtype[1]==1)  // 1 dim
		{
			AAA="A(\\kappa_x;s)";
			if(eqtype[7]==1)
				nonhomf="\\\\ \\hspace*{2.6in} \\times  \\left(\\frac{F_{interior}(x;s)+\\Psi(x,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(x,t=0)}{\\kappa_x^2+s^2}\\right)";
			else
				nonhomf="\\\\ \\hspace*{2.6in} \\times  \\frac{\\Psi(x,t=0)+s\\frac{\\partial \\Psi}{\\partial t}(x,t=0)}{\\kappa_x^2+s^2}";
		}