Explicit strong stability preserving multistep Runge–Kutta methods
Copyright policy )Explicit strong stability preserving multistep Runge–Kutta methods
High-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep Runge–Kutta strong stability preserving (SSP) time integration methods for use with such discretizations. We prove an upper bound on the SSP coefficient of explicit multistep Runge–Kutta methods of order two and above. Numerical optimization is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are tested on the linear advection and nonlinear Buckley-Leverett equations, and the results for the observed total variation diminishing and/or positivity preserving time-step are presented.
- Széchenyi István University Hungary
- University of Massachusetts System United States
- King Abdullah University of Science and Technology Saudi Arabia
- University of Massachusetts Dartmouth United States
Method of lines for initial value and initial-boundary value problems involving PDEs, multistep Runge-Kutta methods, linear advection, semidiscretization, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, stabilty, Buckley-Leverett equations, positivity preserving, variation diminishing, Initial-boundary value problems for second-order hyperbolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, First-order hyperbolic equations
Method of lines for initial value and initial-boundary value problems involving PDEs, multistep Runge-Kutta methods, linear advection, semidiscretization, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, stabilty, Buckley-Leverett equations, positivity preserving, variation diminishing, Initial-boundary value problems for second-order hyperbolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, First-order hyperbolic equations
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