Update the Fields on Welcome Page of Publishing on Web

//here getting current web for now but can be open any web
SPweb currentWeb = SPContext.Current.Web;

//Publishing web instance
PublishingWeb publishingWeb = null;

//Verifying publishing web
if (PublishingWeb.IsPublishingWeb(web))
{
          publishingWeb = PublishingWeb.GetPublishingWeb(web);
 }

//welcome page
SPFile defaultpage = publishingWeb.DefaultPage;

//update field which you want. replace <field internal name> with your field  //internal name

defaultpage.ListItemAllFields[<field internal name>] = value to be updated;

//use SystemUpdate() so that page version will not be increased
defaultpage.ListItemAllFields.SystemUpdate(false);