PetrusW
From Speedsolving.com Wiki

PetrusW is a method for solving the 3x3x3 cube invented by WarriorCatCuber in 2020. The method is a variant on the Petrus method and is efficient enough to be used for advanced speedsolving.
Steps
The steps are as follows:
 2x2x2: Solve a 2x2x2 block in the back of the cube
 2x2x3: Expand the 2x2x2 block into a 2x2x3 block, also on the back of the cube
 EO: Fix the misoriented edges on the cube with ZZstyle EO (Edges oriented relative to where it belongs on the U, F, and D layers)
 L2P: Solve the final two corneredge pairs while only using R, U, L and F2 moves to preserve EO.You can also use the M' U2 M sequence.. This leaves only the last layer and the DownFront edge piece to be solved
 COLL: Solve the remaining 4 corners while preserving EO using COLL
 L5EP: Permute the final five edges with L5EP as in Portico
Pros
 Very few cube rotations are required; if you are able to plan your 2x2x3 in inspection, the number drops to zero
 EO is more free than in Petrus
 L2P has less regrips than in Petrus F2L
Cons
 Just like in Petrus, you cannot look into EO during inspection time
 L5EP has slightly more algorithms than EPLL
 Unlike in Petrus or ZZ, you cannot easily solve the last layer in one look
History
PetrusW was originally proposed on the SpeedSolving Forums by user WarriorCatCuber on February 6, 2020. According to the creator, the idea came from a misinterpretation of another user's critique of a solve with the Petrus Method. After some thought and improvement, WarriorCatCuber decided to show the other forum users his new idea.
Variants
 CLP: After preparing the last CornerEdge Pair for insertion, CLP can be used to orient and permute corners while finishing L2P, skipping the COLL step
 WV/SV + HKPLL: After preparing the last Pair for insertion, Winter Variation or Summer Variation can be used to orient the corners while finishing L2P. Then HKPLL can be used to permute the remaining 4 corners and 5 edges
 HK: After L2P, use the subsets of HKOLL where edges are already oriented, then use HKPLL to permute the remaining 4 corners and 5 edges. (This is similar to the Hawaiian Kociemba Method)
 F2L: Instead of only solving the left and right pairs, all of F2L is completed, allowing for a better finish. This makes the Last Layer easier, but reduces L2P efficiency
 PetrusWC: During the Last slot, ZZc OLS is used to reduce the cube to HKPLL.