Optimized high-order splitting methods for some classes of parabolic equations
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Publication:2840621
DOI10.1090/S0025-5718-2012-02657-3zbMath1278.65075arXiv1102.1622MaRDI QIDQ2840621
Philippe Chartier, Fernando Casas, Sergio Blanes, Ander Murua
Publication date: 23 July 2013
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1102.1622
One-parameter semigroups and linear evolution equations (47D06) Numerical methods for initial value problems involving ordinary differential equations (65L05) Linear differential equations in abstract spaces (34G10) Numerical solutions to abstract evolution equations (65J08)
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Cites Work
- Unnamed Item
- Splitting methods for partial differential equations with rough solutions. Analysis and Matlab programs
- Splitting methods with complex times for parabolic equations
- High order splitting methods for analytic semigroups exist
- Strang's formula for holomorphic semi-groups
- Error bounds for exponential operator splittings
- On the necessity of negative coefficients for operator splitting schemes of order higher than two
- Splitting and composition methods in the numerical integration of differential equations
- Splitting methods with complex coefficients
- On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
- Exponential splitting for unbounded operators
- High-Order Exponential Operator Splitting Methods for Time-Dependent Schrödinger Equations
- Solving Linear Partial Differential Equations by Exponential Splitting
- Some general implicit processes for the numerical solution of differential equations
- General theory of fractal path integrals with applications to many-body theories and statistical physics
- Convergence Analysis for Operator-Splitting Methods Applied to Conservation Laws with Stiff Source Terms
- Order conditions for numerical integrators obtained by composing simpler integrators
- Error Bounds for Fractional Step Methods for Conservation Laws with Source Terms
- Nth-Order Operator Splitting Schemes and Nonreversible Systems
- An algebraic theory of order
- Geometric Numerical Integration
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