Is it possible to fast al-ayyaam al-beed based on the dates published in newspapers or calendars?
Question

                I am well aware that al-ayyaam al-beed are the thirteenth, fourteenth and fifteenth of every hijri month, and that they should be defined on the basis of sighting the new moon, not on the basis of calendars. But my question is: how can I find out when the new month has begun on the basis of sighting the new moon, which is not announced except in the case of Ramadan and Hajj? Can I rely on the date which you put beneath the banner of the website? Especially since I have compared it with the calendars of Umm al-Qura and others, and I found that all the calendars are in harmony with one another, whereas your website is one day ahead of them, therefore I thought that you put the date according to moon-sighting as prescribed in sharee‘ah rather than based on calendars?
Praise be to Allah.
    Al-ayyaam al-beed are the thirteenth, fourteenth and 
    fifteenth of every hijri month. A hadeeth concerning them was narrated by 
    Abu Dharr (may Allah be pleased with him) who said: The Messenger of Allah 
    (blessings and peace of Allah be upon him) said to me: “If you fast any day 
    of the month, then fast on the thirteenth, fourteenth and fifteenth.” 
    Narrated by at-Tirmidhi (761) and an-Nasaa’i (2424); classed as saheeh by 
    al-Albaani in Saheeh at-Targheeb (1038). 

    The beginning of the month is known from sighting of the new 
    moon. If it is possible to ask those who are involved in moon-sighting at 
    the beginning of each month, then that is good. Or you can rely on the moon 
    sighting in some countries which announce it every month. Otherwise, one may 
    fast on the basis of calendars, as it is acceptable to base one’s actions on 
    what is most likely to be the case. 

    Shaykh Ibn Baaz (may Allah have mercy on him) was asked:

    It is no secret that people are not aware of the beginning of 
    the ordinary months, so what is the situation with regard to fasting 
    al-ayyaam al-beed every month? What I mean is: how can a person know when 
    these days are so that he may fast at that time? I hope that you can advise 
    us, may Allah reward you with good. 

    He replied: It is allowed to fast on those days according to 
    calendars, acting on what appears most likely to be the case. If he observes 
    this fast on other days, that is acceptable, because the Prophet (blessings 
    and peace of Allah be upon him) encouraged doing these fasts in every month, 
    but he did not limit it to al-ayaam al-beed, as it is narrated in 
    as-Saheehayn from the Messenger of Allah (blessings and peace of Allah 
    be upon him) that he said to ‘Abdullah ibn ‘Amr ibn al-‘Aas (may Allah be 
    pleased with him): “Fast three days of every month, for a good deed brings a 
    tenfold reward, and that will be like fasting for a lifetime.” In 
    as-Saheehayn it is narrated that Abu Hurayrah (may Allah be pleased with 
    him) said: The Messenger of Allah (blessings and peace of Allah be upon him) 
    advised me to do three things: to fast three days of every month, to offer 
    two rak‘ahs of Duha prayer, and to pray Witr before sleeping. And there are 
    many hadeeths concerning this matter. The individual has the choice: if he 
    wishes he may do them together (consecutively), or if he wishes he may 
    separate them, because the hadeeths are general in meaning and do not 
    specify that these fasts must be done consecutively. And Allah is the source 
    of strength.

    End quote from Majmoo‘ Fataawa Ibn Baaz (15/282) 

    If we assume that we were mistaken about one of these days, 
    that does not matter; rather there is the hope that the one who fasts will 
    be granted the reward in full, because he has an excuse and he did what he 
    was able to. 

    Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 
    Fasting three days of every month is Sunnah. The Prophet (blessings and 
    peace of Allah be upon him) said that fasting three days of every month is 
    like fasting for an entire lifetime. But it is preferable to do that on the 
    ayaam al-beed: the thirteenth, fourteenth and fifteenth of the month. If 
    that is not possible because a woman has her period, or because the 
    individual is travelling or has a guest or gets tired or is sick, and the 
    like, then the reward may also be obtained by the one who fasts days others 
    than these three. ‘Aa’ishah (may Allah be pleased with her) said: The 
    Prophet (blessings and peace of Allah be upon him) used to fast on three 
    days of every month and he would not mind whether he fasted them at the 
    beginning of the month, or in the middle, or at the end. So this matter is 
    broad in scope. Fasting three days of every month is Sunnah, whether that is 
    at the beginning of the month or in the middle or at the end. But if it is 
    during the three ayaam al-beed, that is preferable. But if he was unable to 
    fast because of some reason or need, then we hope that Allah, may He be 
    exalted, will decree reward for everyone who has the habit of fasting these 
    days, but is not able to do so because there was some reason for that.

    End quote from Fataawa Noor ‘ala ad-Darb. 

    With regard to our website, the date on it is based on 
    calendars, except in the case of Ramadan and Dhu’l-Hijjah. 

    And Allah knows best.