Linearly Implicit Multistep Methods for Time Integration

Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators desirable their stability properties, significantly relaxing restrictions on timestep size. However, implicit require solutions to one or more systems nonlinear equations at each timestep, which large simulations can be prohibitively expensive. This paper introduces a new family linearly multistep (LIMM), only requires the solution linear system per timestep. Order conditions theory these presented, as well design implementation considerations. Practical order up five developed that have similar error coefficients, but improved regions, when compared widely used BDF methods. Numerical testing self-starting variable stepsize LIMM shows measurable performance improvement over implementation.