Correct derivatives in Burgers equation (#389)

* Correct derivatives in Burgers equation

Author: HGangloff

docs/source/_rst/tutorials/tutorial12/tutorial.rst

@@ -132,8 +132,8 @@ parameter :math:`\nu`:
             self.nu = nu 
         
             def equation(input_, output_):
-                    return grad(output_, input_, d='x') +\
-                           output_*grad(output_, input_, d='t') -\
+                    return grad(output_, input_, d='t') +\
+                           output_*grad(output_, input_, d='x') -\
                            self.nu*laplacian(output_, input_, d='x')
     
                 

tutorials/tutorial12/tutorial.ipynb

@@ -161,8 +161,8 @@
     "        self.nu = nu \n",
     "    \n",
     "        def equation(input_, output_):\n",
-    "                return grad(output_, input_, d='x') +\\\n",
-    "                       output_*grad(output_, input_, d='t') -\\\n",
+    "                return grad(output_, input_, d='t') +\\\n",
+    "                       output_*grad(output_, input_, d='x') -\\\n",
     "                       self.nu*laplacian(output_, input_, d='x')\n",
     "\n",
     "            \n",

tutorials/tutorial12/tutorial.py

@@ -113,7 +113,7 @@ def __init__(self, nu = 0.):
         self.nu = nu 
 
         def equation(input_, output_):
-                return grad(output_, input_, d='x') +                       output_*grad(output_, input_, d='t') -                       self.nu*laplacian(output_, input_, d='x')
+                return grad(output_, input_, d='t') +                       output_*grad(output_, input_, d='x') -                       self.nu*laplacian(output_, input_, d='x')
 
 
         super().__init__(equation)