An Algebraic Theory of Integration Methods
From MaRDI portal
Publication:5674336
DOI10.2307/2004720zbMath0258.65070OpenAlexW4243107850MaRDI QIDQ5674336
Publication date: 1972
Full work available at URL: https://doi.org/10.2307/2004720
Trees (05C05) Theoretical approximation of solutions to ordinary differential equations (34A45) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical analysis in abstract spaces (65J99)
Related Items
Multi-step Nyström methods for general second-order initial value problemsy″(t) =f(t,y(t),y′(t)), Runge–Kutta Methods for Ordinary Differential Equations, An operadic approach to substitution in Lie–Butcher series, Algebraic deformation for (S)PDEs, Discontinuous Galerkin Methods for Ordinary Differential Equations, Post-Lie algebras in Regularity Structures, Deterministic dynamics and randomness in PDE. Abstracts from the workshop held May 22--28, 2022, Rough paths and SPDE, The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators, A New Optimality Property of Strang’s Splitting, Strong stability-preserving three-derivative Runge-Kutta methods, Quasi-geometric rough paths and rough change of variable formula, Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation, The Lie derivative and Noether's theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators, An algebraic approach to Runge-Kutta methods, Doubling pre-Lie algebra of rooted trees, Rooted Tree Graphs and the Butcher Group: Combinatorics of Elementary Perturbation Theory, On Some Tree-Indexed Series with One and Two Parameters, Arborified Multiple Zeta Values, Unnamed Item, A Convergence Criterion for a Class of Integration Methods, A Characterization of Energy-Preserving Methods and the Construction of Parallel Integrators for Hamiltonian Systems, A note on Radau and Lobatto formulae for O.D.E.: s, An algebraic theory of order, The number of conditions for a Runge-Kutta method to have effective order \(p\), Runge-Kutta methods: Some historical notes, Aromatic Butcher series, Invariant Connections, Lie Algebra Actions, and Foundations of Numerical Integration on Manifolds, Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs, Algebraic structures and stochastic differential equations driven by Lévy processes, The support of singular stochastic partial differential equations, Resonance-based schemes for dispersive equations via decorated trees, The Order of Numerical Methods for Ordinary Differential Equations, Post-Lie Magnus expansion and BCH-recursion, Doubling bialgebras of rooted trees, A formal series approach to the center manifold theorem, Generalized symmetric Runge-Kutta methods, Solving directly special fourth-order ordinary differential equations using Runge-Kutta type method, Continuous stage stochastic Runge-Kutta methods, A renormalized rough path over fractional Brownian motion, A class of Rosenbrock-type schemes for second-order nonlinear systems of ordinary differential equations, Ramification of rough paths, Trees and numerical methods for ordinary differential equations, On explicit two-derivative Runge-Kutta methods, Decomposition spaces, incidence algebras and Möbius inversion. I: Basic theory, Order conditions for integrators and mappings with applications, Renormalisation from non-geometric to geometric rough paths, A simplified Nyström-tree theory for extended Runge-Kutta-Nyström integrators solving multi-frequency oscillatory systems, Multi-step hybrid methods for special second-order differential equations \(y^{\prime \prime}(t)=f(t,y(t))\), Lie-Butcher theory for Runge-Kutta methods, Pathlike co/bialgebras and their antipodes with applications to bi- and Hopf algebras appearing in topology, number theory and physics, Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths, The dichotomy of stiffness: Pragmatism versus theory, Renormalising SPDEs in regularity structures, On post-Lie algebras, Lie-Butcher series and moving frames, Efficiently implementable multivalue methods for solving stiff ordinary differential equations, An improved tri-coloured rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems, Computing of B-series by automatic differentiation, The tridendriform structure of a discrete Magnus expansion, Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods, Runge-Kutta methods on Lie groups, Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds, Variational principles for fluid dynamics on rough paths, A comodule-bialgebra structure for word-series substitution and mould composition, The tree and forest spaces with applications to initial-value problem methods, The cohesiveness of G-symplectic methods, The Magnus expansion, trees and Knuth's rotation correspondence, Palindromic 3-stage splitting integrators, a roadmap, Categorification of Hopf algebras of rooted trees., Ramification of Volterra-type rough paths, QED Hopf algebras on planar binary trees., A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK), The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations, Order conditions for numerical methods for partitioned ordinary differential equations, Runge-Kutta methods and Banach algebras, B-series analysis of iterated Taylor methods, Backward error analysis and the substitution law for Lie group integrators, Algebraic structures of B-series, On explicit two-derivative two-step Runge-Kutta methods, Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees., Direct integrators of Runge-Kutta type for special third-order ordinary differential equations, An energy-preserving exponentially-fitted continuous stage Runge-Kutta method for Hamiltonian systems, A theory of regularity structures, Relations between the Hopf algebra and the B-series with new concepts, Two-derivative Runge-Kutta methods for PDEs using a novel discretization approach, Partitioned exponential methods for coupled multiphysics systems, Construction of symplectic (partitioned) Runge-Kutta methods with continuous stage, Subquadrature expansions for TSRK methods, Modified ROW methods for stiff problems, New directions in rough path theory. Abstracts from the workshop held December 6--12, 2020 (online meeting), Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials, On eigenvalues of a matrix arising in energy-preserving/dissipative continuous-stage Runge-Kutta methods, Derivation of three-derivative Runge-Kutta methods, Hamiltonian B-series and a Lie algebra of non-rooted trees, Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation, The Lie group structure of the Butcher group, Enhanced order composition methods, A construction of the rough path above fractional Brownian motion using Volterra's representation, Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case, A note on continuous-stage Runge-Kutta methods, Multi-step hybrid methods adapted to the numerical integration of oscillatory second-order systems, On the Butcher group and general multi-value methods, Geometric versus non-geometric rough paths, Two interacting Hopf algebras of trees: a Hopf-algebraic approach to composition and substitution of B-series., A rough path over multidimensional fractional Brownian motion with arbitrary Hurst index by Fourier normal ordering, The incidence comodule bialgebra of the Baez-Dolan construction, An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants, Hölder-continuous rough paths by Fourier normal ordering, Lagrange inversion and combinatorial species with uncountable color palette, High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods, The recursions of order conditions for some Runge-Kutta-like methods, B-series methods are exactly the affine equivariant methods, Hopf algebra structure of generalized quasi-symmetric functions in partially commutative variables, Multi-step Runge-Kutta-Nyström methods for special second-order initial value problems, General linear methods for ordinary differential equations, Algebraic structure of aromatic B-series, On an extension of Knuth's rotation correspondence to reduced planar trees, Free nonunitary Rota-Baxter family algebras and typed leaf-spaced decorated planar rooted forests, On symmetrizers for Gauss method, Explicit integrator of Runge-Kutta type for direct solution of \(u^{(4)} = f(x, u, u', u)\), Symmetric two-step algorithms for ordinary differential equations, An application of the Runge-Kutta space, Trees and B-series, Energy-preserving trigonometrically fitted continuous stage Runge-Kutta-Nyström methods for oscillatory Hamiltonian systems, On the order of general linear methods, The universal pre-Lie-Rinehart algebras of aromatic trees, Constructing general rough differential equations through flow approximations, Runge-Kutta-methods with expansion in even powers of h, A remainder estimate for branched rough differential equations, Energy conservation with non-symplectic methods: examples and counter-examples, Numerical methods for ordinary differential equations in the 20th century, Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization, Combinatorics of (perturbative) quantum field theory
Cites Work