A New Robust Numerical Scheme for Nonlinear ODE Systems

To solve ODEs systems, implicit numerical schemes are often used because of their good stability. Among the most widely used implicit methods for stiff problem are Backward Differentiation Formulas (BDF). However, solving implicit time stepping requires the use of Newton's algorithm which can be very consuming CPU-time. Then, in this paper, we propose a linearly-implicit method built from BDF scheme and which keeps a good stability. The scheme is based on a linearization of the BDF implicit term and the use of an interpolation of right order. The method obtained is linear for each time step and thus faster that the Newton method. Numerical tests on a challenging real-world test problem reveal that the method proposed is a promising alternative to well-established approaches based on Newton algorithm