Powershell script to Delete Document By Name in SharePoint 2010

Below is the Powershell script to delete document by Name from Document Library

[System.Reflection.Assembly]::LoadWithPartialName("Microsoft.SharePoint")

$site = new-object Microsoft.SharePoint.SPSite("http:// sharepoint-site-url ")

$web = $site.openweb()

$list=$web.Lists["Document-Library-Name "]

$listItems = $list.Items

$listItemsTotal = $listItems.Count

Write-Host $listItemsTotal

for ($x=$listItemsTotal-1;$x -ge 0; $x--)

{

  if($listItems[$x].name.Contains("file")) # file refers to the    name of the document

  {

    Write-Host("DELETED: " + $listItems[$x].name)

    $listItems[$x].Delete()

  }

}