Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
Applied Numerical Mathematics - Special issue on time integration
A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
SIAM Journal on Scientific Computing
Approximate factorization for time-dependent partial differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Linearly implicit Runge—Kutta methods for advection—reaction—diffusion equations
Applied Numerical Mathematics
Operator splitting and approximate factorization for taxis-diffusion-reaction models
Applied Numerical Mathematics
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Linearly implicit Runge-Kutta methods are a class of suitable time integrators for initial value problems of ordinary differential systems whose right-hand side function can be written as the sum of a stiff linear part and a nonlinear term. Such systems arise for instance after spatial discretization of taxis-diffusion-reaction systems from mathematical biology. When approximate matrix factorization is used for efficiently solving the stage equations appearing in these methods, then the order of the methods is reduced to one. In this paper we analyse this fact and propose an appropriate and efficient correction to achieve order two while preserving the main stability properties of the underlying method. Numerical experiments with LIRK3 [Appl. Numer. Math. 37 (2001) 535] illustrating the theory are provided. In the case of taxis-diffusion-reaction systems, the corrected method compares well with other suitable schemes.