After he (Abraham) had patiently endured, he obtained the promise. (Hebrew 6:15)
For you have need of patience, that, after you have done the will of God, you might receive the promise. (Hebrews 10:36)
Patience is one of the requirements to receiving results in prayer. Even if it is something God has promised, we must do the will of God and have patience, if we are to receive the promised results.
Patience is constant, unwavering faith. It is believing without wavering that God is a reliable source of the result we are seeking. It is believing without wavering that God is a source that can be trusted to answer the prayer: he has the supply needed and he won't withhold the supply.
Wavering is related to doubt. It is alternately trusting different sources as evidence of truth: trusting in evidence seen and evidence not seen. Patience starts in faith - belief based on evidence of things not seen - and stays in faith. It relies on God to supply with the same intensity from the beginning until the promise is received - and beyond.
Patience is not just not doubting. Patience takes the first step trusting in God to provide and then with the same trust takes the second, the third, and as many as it takes until the need is provided. Patience is determined calmness. It is like a sea that resists the howling wind of opposing evidence or persecution and stays calm.
James says that the trying of our faith works patience. Our faith - trusting evidence not seen that God will supply our need - is tried in the course of our prayer. Only genuine, true faith works to receive from God. The trying of our faith with opposing evidence of things seen and persecution works patience. It works constant trusting in God and not evidence of things seen.
Let patience have her complete work, that you may be mature and finished, lacking nothing. (James 1:4)
Patience works to receive from God so that we receive what we need to become spiritually mature and complete (our spirit prospers), and we lack nothing (spiritually or materially). If we lack wisdom, we are to ask God and continue in patience until we receive. If we ask it will be given and and if we continue pressing forward in faith we will receive.
We are told that the person who will not press forward in patience should not think that they will receive anything of the Lord. (James 1:7) Blessed is the person who faces opposing evidence and continues to belief without wavering: for when he does he will receive that which the Lord has promised. (James 1:12)
Temptation to Waver vs Wavering
A distinction needs to be made between doubting, or wavering, and the temptation to doubt, or waver. Having a thought of doubt is not necessarily doubting. If it comes from our heart it is, but it could be temptation. We have to ask God which it is and deal with it as he instructs us.