The calculable form of the R-matrix method has been previously shown to be a useful tool in approximately solving the Schrodinger equation in nuclear scattering problems. We use this technique with the Lagrange-mesh method to solve for the wave functions of projectiles in multichannel collisions efficiently. We combine the Woods-Saxon potential, the Perey-Buck potential, and a nonzero coupling potential to computationally solve for the projectile wave function inside the channel radius. Parallel programming techniques are introduced to reduce the computation time required for collisions involving many channels. We conclude that the R-matrix method is an efficient method to predict the wave functions of projectile particles in nuclear scattering problems involving both multiple channels and non-local potentials.