Two algorithms for simulating the response of peptides to sequences of IR pulses are developed and applied to N-methyl acetamide (NMA) and a 17 residue alpha-helical peptide (YKKKH17) in D2O. A fluctuating vibrational-exciton Hamiltonian for the amide I mode is constructed from molecular dynamics trajectories. Coupling with the environment is described using a density functional theory electrostatic map. The cumulant expansion of Gaussian fluctuation incorporates motional narrowing due to fast frequency fluctuations and is adequate for NMA and for isotopically labeled bands in large peptides. Real-space truncation of the scattering matrix of the nonlinear exciton equations significantly reduces the computational cost, making it particularly attractive for slow fluctuations in large globular proteins.