Islam is the religion of easiness. Whenever there is a necessity, the law is relaxed. In case there are differences of opinions among Muslim jurists, the Muslim is encouraged to follow the opinion which best suits him. Here, we would like to stress that Muslim jurists differ concerning performing ablution on a cast or bandage.
According to The Reliance of the Traveler by Ahmad ibn An-Naqib Al-Misri, there are two juristic views concerning the issue raised in the question: The first view is that of the Shafi`is, whose opinion on this matter is the hardest as they insist on full ablution except for the injured part, where a full dry ablution must be performed at the proper point in the ablution sequence in place of washing the injured part. According to them, if someone has a cast, it must be first applied when one has ablution, and thereafter one must wipe it with water when one comes to it in the ablution sequence in addition to performing a complete dry ablution at that point. In addition, when someone with such a bandage recovers and has his cast or dressing removed, he is obliged to make up for (repray) all the prayers he performed with such an ablution.
The other juristic view is attributed to the Hanafis, who maintain that the one who has a bandage that cannot be removed without harm due to medical necessity can simply wipe more than half the bandage when he comes to it in his ablution. He may pray with such an ablution and need not repeat the prayer later.
The Islamic Religious Council of Singapore, issued the following fatwa: For those in a cast, to perform their Prayer, they have to make wudu’ and tayammum. Wudu’ is for the body parts that are not covered with the cast, and tayammum for the part that is covered with the cast.
You can perform your tayammum after or before wudu’. For the wudu’ part, perform it as you normally do. When you reach the part on your casted limb, wipe over it with a wet hand. You need not to reperform your Prayer after the cast is taken off.
To perform the Prayer, do it as you normally do. For the actions that you cannot do because of the cast, you are allowed to do the next best thing. For example, if you cannot bend the leg under you when sitting down, you are allowed to straighten your leg in front of you.