Transformed implicit-explicit second derivative diagonally implicit multistage integration methods with strong stability preserving explicit part (Q2189674)

A new class of implicit-explicit (IMEX) methods are derived for systems of ordinary differential equations with stiff ad nonstiff parts. The non-stiff part is solved by an explicit second derivative diagonally implicit multistage integrator and the stiff part by an implicit diagonally implicit multistage integrator. The implicit part is A-and L-stable and satisfies the Runge-Kutta stability property, whereas the explicit part has strong stability-preserving property. Several methods up to order four are derived. Numerical experiments were performed on one-dimensional linear advection-diffusion, advection-reaction and nonlinear shallow water equations to verify the theoretical results and show the efficiency of the constructed methods.