A node-wise (NS) schedule has been recently proposed for decoding LDPC codes with the linear programming (LP) decoding approach, based on the alternate direction method of multipliers (ADMM). It improves the error correction performances as well as the convergence speed of the ADMM-LP decoder. However, it suffers from a high computational complexity resulted from residuals calculation. In this paper, a new formulation of the ADMM-LP algorithm with a modified computational scheduling is proposed for decoding LDPC convolutional codes. Simulations show that it reduces the computational complexity while improving the error correction performances and speeding up the decoding process. The decoding complexity is further reduced when considering the NS-ADMM approximation which allows savings up to 70% of the residuals calculation.