/* Last updated: December 12, 2020 by Hereman in Boulder */
/* For use with symmgrp2020.max under Maxima */

/* File name: vcheat-run5-case3-Dec12-2020-wh.dat. */
/* Data file for a heat equation with a variable coefficient given in the online manuscript Faruk Gungor. */

/* Case 3: bb = 3/2 and g =!= 0  */ 

/* u_t - x u_xx- bb u_x = 0 */
/* Assign u[1] to u, x[1] to x, x[2] to t, bb is a constant. */

/* number of independent variables: */
p : 2$

/* number of dependent variables: */
q : 1$

/* number of equations in the system: */
m : 1$

warnings: false$
parameters : [bb] $
sublisteqs : [all]$
subst_deriv_of_vi: true$
highest_derivatives : all$

/* no information is given yet -- this will be updated in next runs. */
info_given : true$

depends([eta1,f1,f2],[x[1],x[2]]);
depends([eta2,g,g1],x[2]);

/* Case 3: If b = 3/2 and g =!= zero */

bb : 3/2;

g : c4*x[2]+c5;

g1 : -bb*c1*x[2]+c6;

eta2 : c1*x[2]^2 + c2*x[2] + c3;

eta1 : g*sqrt(x[1])+x[1]*diff(eta2,x[2]);

f1 : -sqrt(x[1])*diff(g,x[2])+((1-2*bb)/(4*sqrt(x[1])))*g-(1/2)*x[1]*diff(eta2,x[2],2)+g1;

gradef(f2,x[2],x[1]*diff(f2,x[1],2)+bb*diff(f2,x[1]));

phi1 : f1*u[1]+f2;

e1 : u[1,[0,1]]-x[1]*u[1,[2,0]]-bb*u[1,[1,0]];
/* bb is just a constant positive parameter */
v1 : u[1,[2,0]];

/* end of data file vcheat-run5-case3-Dec12-2020-wh.dat. */