Reference Work Entry

Encyclopedia of Applied and Computational Mathematics

pp 460-468


Explicit Stabilized Runge–Kutta Methods

  • Assyr AbdulleAffiliated withMathematics Section, École Polytechnique Fédérale de Lausanne (EPFL)


Chebyshev methods; Runge–Kutta–Chebyshev methods


Explicit stabilized Runge–Kutta (RK) methods are explicit one-step methods with extended stability domains along the negative real axis. These methods are intended for large systems of ordinary differential equations originating mainly from semi-discretization in space of parabolic or hyperbolic–parabolic equations. The methods do not need the solution of large linear systems at each step (as, e.g., implicit methods). At the same time due to their extended stability domains along the negative real axis, they have less severe step size restriction than classical explicit methods when solving stiff problems.


For solving time-dependent partial differential equations (PDEs), a widely used approach is to first discretize the space variables to obtain a system of ordinary differential equations (ODEs) of the form ...

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