diff --git a/src/Init/Init_Load_DumpTable.cpp b/src/Init/Init_Load_DumpTable.cpp
index 0307bdf2ac..dc056ab47c 100644
--- a/src/Init/Init_Load_DumpTable.cpp
+++ b/src/Init/Init_Load_DumpTable.cpp
@@ -46,28 +46,46 @@ void Init_Load_DumpTable()
 //    stop the reading
       if ( input_line[0] == 42 )                   // '*' == 42
       {
-
 //       ensure that at least one data dump time is loaded
          if ( line == 0 )
             Aux_Error( ERROR_INFO, "please provide at least one data dump time in the dump table !!\n" );
 
-         DumpTable_NDump   = line;                 // record the number of data dumps
-         DumpTable[line]   = __FLT_MAX__;          // set the next dump as an extremely large number
+         DumpTable_NDump = line;          // record the number of data dumps
+         DumpTable[line] = __FLT_MAX__;   // set the next dump as an extremely large number
 
-         if ( DumpTable[line-1] < END_T )
+//       for END_T < 0.0, reset the ending time as the time of the last dump
+         if ( END_T < 0.0 )
          {
-            END_T          = DumpTable[line-1];    // reset the ending time as the time of the last dump
+            END_T = DumpTable[line-1];
 
             if ( MPI_Rank == 0 )
-               Aux_Message( stdout, "NOTE : the END_T is reset to the time of the last data dump = %13.7e\n",
-                            END_T );
+               Aux_Message( stdout, "NOTE : END_T is reset to the time of the last data dump in %s: %13.7e\n",
+                            FileName, END_T );
          }
 
+//       for END_T >= 0.0, reset the ending time to the largest data dump time not greater than the input END_T
+         else
+         {
+            for (int t=line-1; t>=0; t--)
+            {
+               if ( END_T >= DumpTable[t] )
+               {
+                  END_T = DumpTable[t];
+
+                  if ( MPI_Rank == 0 )
+                     Aux_Message( stdout, "NOTE : END_T is reset to the largest time in %s not greater "
+                                          "than the input END_T: %13.7e\n",
+                                  FileName, END_T );
+                  break;
+               }
+            }
+         } // if ( END_T < 0.0 ) ... else ...
+
 
 //       verify the loaded dump table
          for (int t=1; t<=line; t++)
          {
-            if ( DumpTable[t] < DumpTable[t-1] )
+            if ( DumpTable[t] <= DumpTable[t-1] )
                Aux_Error( ERROR_INFO, "values recorded in \"%s\" must be monotonically increasing !!\n",
                           FileName );
          }
@@ -79,7 +97,7 @@ void Init_Load_DumpTable()
 
 
    if ( line == MaxLine )
-      Aux_Error( ERROR_INFO, "please prepare a symbol * in the end of the file <%s> !!\n", FileName );
+      Aux_Error( ERROR_INFO, "please prepare a * symbol at the end of the file <%s> !!\n", FileName );
 
 
    fclose( File );
@@ -87,6 +105,28 @@ void Init_Load_DumpTable()
    if ( input_line != NULL )     free( input_line );
 
 
+// insert initial time Time[0]
+   for (int t=0; t<DumpTable_NDump; t++)
+   {
+//    check if the initial time is already in the dump table
+      if (   (  Time[0] != 0.0 && fabs( (Time[0]-DumpTable[t])/Time[0] ) < 1.0e-8   )  ||
+             (  Time[0] == 0.0 && fabs(  Time[0]-DumpTable[t]          ) < 1.0e-12  )      )    break;
+
+//    insert the initial time into the dump table
+      if (  ( Time[0] < DumpTable[t] )  &&  ( t == 0 || Time[0] > DumpTable[t-1] )  )
+      {
+         for (int s=DumpTable_NDump; s>t; s--)  DumpTable[s] = DumpTable[s-1];
+         DumpTable[t] = Time[0];
+         DumpTable_NDump ++;
+
+         if ( MPI_Rank == 0 )
+            Aux_Message( stdout, "NOTE : initial time %13.7e is inserted into the dump table\n", Time[0] );
+
+         break;
+      }
+   }
+
+
    if ( MPI_Rank == 0 )    Aux_Message( stdout, "Init_Load_DumpTable ... done\n" );
 
 } // FUNCTION : Init_Load_DumpTable
diff --git a/src/Output/Output_DumpData.cpp b/src/Output/Output_DumpData.cpp
index 8a319031a0..b5cee8364e 100644
--- a/src/Output/Output_DumpData.cpp
+++ b/src/Output/Output_DumpData.cpp
@@ -56,9 +56,9 @@ void Output_DumpData( const int Stage )
                DumpTime = round( int(Time[0]/OUTPUT_DT) + 1.0 )*OUTPUT_DT;
 
 //             be careful about round-off errors
-               if (   (  DumpTime <= Time[0]  )                                            ||
-                      (  Time[0] != 0.0 && fabs( (Time[0]-DumpTime)/Time[0] ) < 1.0e-8  )  ||
-                      (  Time[0] == 0.0 && fabs(  Time[0]-DumpTime          ) < 1.0e-12 )      )   DumpTime += OUTPUT_DT;
+               if (   (  DumpTime <= Time[0]  )                                             ||
+                      (  Time[0] != 0.0 && fabs( (Time[0]-DumpTime)/Time[0] ) < 1.0e-8   )  ||
+                      (  Time[0] == 0.0 && fabs(  Time[0]-DumpTime          ) < 1.0e-12  )      )  DumpTime += OUTPUT_DT;
             }
          }
          break;
@@ -71,9 +71,9 @@ void Output_DumpData( const int Stage )
                {
                   DumpTime = DumpTable[DumpTableID];
 
-                  if (   (  DumpTime >= Time[0]  )                                            ||
-                         (  Time[0] != 0.0 && fabs( (Time[0]-DumpTime)/Time[0] ) < 1.0e-8  )  ||
-                         (  Time[0] == 0.0 && fabs(  Time[0]-DumpTime          ) < 1.0e-12 )      )   break;
+                  if (   (  DumpTime >= Time[0]  )                                             ||
+                         (  Time[0] != 0.0 && fabs( (Time[0]-DumpTime)/Time[0] ) < 1.0e-8   )  ||
+                         (  Time[0] == 0.0 && fabs(  Time[0]-DumpTime          ) < 1.0e-12  )      )  break;
                }
             }