Purgatory is something that, in essence, the Eastern Orthodox believe in...though they do not use the word "purgatory" to describe it. Like many doctrinal points, when they are in anti-Latin mode the Eastern Orthodox tend to deny any similarity between their belief in the afterlife and the Catholic purgatory.
To claim similarity between the Orthodox partial judgment at the Catholic purgatory is to express an extreme level of misunderstanding either of the Catholic teaching, the Orthodox teaching, or both.
They don't claim purgatory to be the same as the partial judgement, they claim their particular judgement to be the same as our partial judgement, the two judhgements are similar but not the same because RC teaches that judgement to be unchangeable where the Orthodox accept the possibility of change.
Now to purgatory. They claim it to be something similar to...
And such as though envolved in mortal sins have not departed in despair, but have, while still living in the body, repented, though without bringing forth any fruits of repentance — by pouring forth tears, forsooth, by kneeling while watching in prayers, by afflicting themselves, by relieving the poor, and in fine {in summation ELC} by shewing forth by their works their love towards God and their neighbour, and which the Catholic Church hath from the beginning rightly called satisfaction — of these and such like the souls depart into Hades, and there endure the punishment due to the sins they have committed. But they are aware of their future release from thence, and are delivered by the Supreme Goodness, through the prayers <152> of the Priests, and the good works which the relatives of each do for their Departed; especially the unbloody Sacrifice availing in the highest degree; which each offereth particularly for his relatives that have fallen asleep, and which the Catholic and Apostolic Church offereth daily for all alike; it being, of course, understood that we know not the time of their release. For that there is deliverance for such from their direful condition, and that before the common resurrection and judgment we know and believe; but when we know not.
and...
376. What is to be remarked of such souls as have departed with faith, but without having had time to bring forth fruits worthy of repentance?
This: that they may be aided towards the attainment of a blessed resurrection by prayers offered in their behalf, especially such as are offered in union with the oblation of the bloodless sacrifice of the Body and Blood of Christ, and by works of mercy done in faith for their memory.
377. On what is this doctrine grounded?
On the constant tradition of the Catholic Church; the sources of which may be seen even in the Church of the Old Testament. Judas Maccabæus offered sacrifice for his men that had fallen. 2 Macc. xii. 43. Prayer for the departed has ever formed a fixed part of the divine Liturgy, from the first Liturgy of the Apostle James. St. Cyril of Jerusalem says: Very great will be the benefit to those souls for which prayer is offered at the moment when the holy and tremendous Sacrifice is lying in view. (Lect. Myst. v. 9.)
St. Basil the Great, in his prayers for Pentecost, says that the Lord vouchsafes to receive from us propitiatory prayers and sacrifices for those that are kept in Hades, and allows us the hope of obtaining for them peace, relief, and freedom.
and...
But if souls have departed this life in faith and love, while nevertheless carrying away with themselves certain faults, whether small ones over which they have no repented at all, or great ones for which--even though they have repented over them--they did not undertake to show fruits of repentance: such souls, we believe, must be cleansed from this kind of sins, but not by means of some purgatorial fire or a definite punishment in some place (for this, as we have said, has not at all be handed down to us). But some must be cleansed in the very departure from the body, thanks only to fear, as St. Gregory the Dialogist literally shows; while others must be cleansed after the departure from the body, either while remaining in the same earthly place, before they come to worship God and are honored with the lot of the blessed, or--if their sins were more serious and bind them for a longer duration--they are kept in [hades], but not in order to remain forever in fire and torment, but as it were in prison and confinement under guard.
All such ones, we affirm, are helped by the prayers and Liturgies performed for them, with the cooperation of the Divine goodness and love for mankind. This Divine cooperation immediately disdains and remits some sins, those committed out of human weakness, as Dionysius the Great (the Areopagite) says in 'Reflections on the Mystery of Those Reposed in Faith' (In 'The Ecclesiastical Hierarchy, 7, 7); while other sins, after a certain time, by righteous judgments it either likewise releases and forgives--and that completely--or lightens the responsibility for them until that final judgment. And therefore we see no necessity whatever for any other punishment or for a cleansing fire; for some are cleansed by fear, while others are devoured by gnawings of conscience with more torment than any fire, and still others are cleansed only the the very terror before the Divine Glory and the uncertainty as to what the future will be...
And so, we intreat God and believe to deliver the departed from (eternal torment), and not from any other torment or fire apart from those torments and that fire which have been proclaimed to be forever. And that, moreover, the souls of the departed are delivered by prayers from confinement in [hades], as if from a certain prison, is testified, among many others, by Theophanes the Confessor, called the Branded. ...In one of the canons for the reposed he thus prays for them: 'Deliver, O Savior, Thy slaves who are in the [hades] of tears and sighing' (Octoechos, Saturday canon for the deposed, Tone 8, Canticle 6, Glory).
-- St. Mark of Ephesus, First Homily on the Refutation of the Latin Chapters Concerning Purgatorial Fire
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