Superconvergence analysis of symmetric Gauss-type exponential collocation integrators for solving the multidimensional nonlinear first-order partial differential equations

The main objective of this research is to develop and analyze high-order symmetric Gauss-type exponential collocation time-stepping methods for solving systems of nonlinear first-order partial differential equations (PDEs). Initially, the nonlinear PDEs are reformulated as an abstract Hamiltonian or...

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Vydáno v:Journal of mathematical chemistry Ročník 63; číslo 10; s. 2023 - 2050
Hlavní autoři: Wu, Xiumei, Fang, Yonglei, Liu, Changying, Song, Yuanling
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.11.2025
Springer Nature B.V
Témata:
Accuracy
Boundary conditions
Chemistry
Chemistry and Materials Science
Collocation
Collocation methods
Eigenvectors
Function space
Hamiltonian functions
Hilbert space
Integrators
Math. Applications in Chemistry
Nonlinear differential equations
Nonlinear systems
Ordinary differential equations
Original Paper
Parabolic differential equations
Partial differential equations
Physical Chemistry
Symmetry
Theoretical and Computational Chemistry
65L05
65L06
34C14
Nonlinear first-order PDEs
65L70
Variation-of-constants formula
Exponential integrator
65L20
Superconvergence
Abstract ordinary differential equation
Symmetry
ISSN:0259-9791, 1572-8897
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Popis
Shrnutí:The main objective of this research is to develop and analyze high-order symmetric Gauss-type exponential collocation time-stepping methods for solving systems of nonlinear first-order partial differential equations (PDEs). Initially, the nonlinear PDEs are reformulated as an abstract Hamiltonian ordinary differential equation (ODE) system in an appropriate infinite-dimensional function space. Subsequently, the Gauss-type exponential collocation time integrators are derived. The symmetry, local error bounds and nonlinear stability of the proposed time integrators are rigorously analysed in details. Furthermore, the rigourous convergence analysis demonstrates that Gauss-type exponential collocation time integrators can achieve superconvergence. Numerical experiments verify our theoretical analysis results, and demonstrate the remarkable superiority in comparison with the traditional temporal integration methods.
Bibliografie:ObjectType-Article-1
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ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-025-01754-5