Jacobian-Free Explicit Multiderivative Runge–Kutta Methods for Hyperbolic Conservation Laws

[1]  Jochen Schütz,et al.  Parallel-in-Time High-Order Multiderivative IMEX Solvers , 2021, Journal of Scientific Computing.

[2]  P. Mulet,et al.  On approximate implicit Taylor methods for ordinary differential equations , 2020, Computational and Applied Mathematics.

[3]  David Zorío,et al.  Lax-Wendroff Approximate Taylor Methods with Fast and Optimized Weighted Essentially Non-oscillatory Reconstructions , 2020, J. Sci. Comput..

[4]  Hugo Carrillo,et al.  Compact Approximate Taylor Methods for Systems of Conservation Laws , 2019, Journal of Scientific Computing.

[5]  Michael Dumbser,et al.  Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine , 2018, Axioms.

[6]  R. LeVeque,et al.  Numerical Methods for Conservation Laws: From Analysis to Algorithms , 2017 .

[7]  Antonio Baeza,et al.  An Approximate Lax–Wendroff-Type Procedure for High Order Accurate Schemes for Hyperbolic Conservation Laws , 2017, J. Sci. Comput..

[8]  Alexander Jaust,et al.  Implicit Multiderivative Collocation Solvers for Linear Partial Differential Equations with Discontinuous Galerkin Spatial Discretizations , 2017, Journal of Scientific Computing.

[9]  Jiequan Li,et al.  A Two-Stage Fourth Order Time-Accurate Discretization for Lax-Wendroff Type Flow Solvers I. Hyperbolic Conservation Laws , 2015, SIAM J. Sci. Comput..

[10]  Alexander Jaust,et al.  Implicit Multistage Two-Derivative Discontinuous Galerkin Schemes for Viscous Conservation Laws , 2015, J. Sci. Comput..

[11]  Wei Guo,et al.  A New Lax–Wendroff Discontinuous Galerkin Method with Superconvergence , 2015, J. Sci. Comput..

[12]  Zachary Grant,et al.  Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes , 2015, J. Sci. Comput..

[13]  Andrew J. Christlieb,et al.  High-Order Multiderivative Time Integrators for Hyperbolic Conservation Laws , 2013, J. Sci. Comput..

[14]  Jianxian Qiu,et al.  Simulations of Shallow Water Equations with Finite Difference Lax-Wendroff Weighted Essentially Non-oscillatory Schemes , 2011, J. Sci. Comput..

[15]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[16]  Robert P. K. Chan,et al.  On explicit two-derivative Runge-Kutta methods , 2010, Numerical Algorithms.

[17]  William E. Schiesser,et al.  Linear and nonlinear waves , 2009, Scholarpedia.

[18]  Michael Dumbser,et al.  A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes , 2008, J. Comput. Phys..

[19]  Michael Dumbser,et al.  Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws , 2008, J. Comput. Phys..

[20]  Michael Dumbser,et al.  The discontinuous Galerkin method with Lax-Wendroff type time discretizations , 2005 .

[21]  Eleuterio F. Toro,et al.  ADER schemes for three-dimensional non-linear hyperbolic systems , 2005 .

[22]  Claus-Dieter Munz,et al.  ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D , 2002, J. Sci. Comput..

[23]  Eleuterio F. Toro,et al.  ADER: Arbitrary High Order Godunov Approach , 2002, J. Sci. Comput..

[24]  Chi-Wang Shu,et al.  Finite Difference WENO Schemes with Lax-Wendroff-Type Time Discretizations , 2002, SIAM J. Sci. Comput..

[25]  Steven J. Ruuth,et al.  A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods , 2002, SIAM J. Numer. Anal..

[26]  P. Lax,et al.  Systems of conservation laws , 1960 .

[27]  Zachary J. Grant,et al.  HIGH ORDER UNCONDITIONALLY STRONG STABILITY PRESERVING MULTI-DERIVATIVE IMPLICIT AND IMEX RUNGE–KUTTA METHODS WITH ASYMPTOTIC PRESERVING PROPERTIES , 2021 .

[28]  Turgut Özis,et al.  Derivation of three-derivative Runge-Kutta methods , 2016, Numerical Algorithms.

[29]  Angelika Fruehauf,et al.  A First Course In Numerical Analysis , 2016 .

[30]  Oleg A. Yakimenko,et al.  Symbolic Math Toolbox , 2010 .

[31]  E. Hairer,et al.  Solving Ordinary Differential Equations II , 2010 .

[32]  Jianxian Qiu,et al.  Development and Comparison of Numerical Fluxes for LWDG Methods , 2008 .

[33]  J. Strikwerda Finite Difference Schemes and Partial Differential Equations, Second Edition , 2004 .

[34]  Chi-Wang Shu,et al.  Strong Stability-Preserving High-Order Time Discretization Methods , 2001, SIAM Rev..

[35]  George Em Karniadakis,et al.  The Development of Discontinuous Galerkin Methods , 2000 .

[36]  高等学校計算数学学報編輯委員会編 高等学校計算数学学報 = Numerical mathematics , 1979 .

[37]  A. Ralston A first course in numerical analysis , 1965 .