A new piecewise reproducing kernel function algorithm for solving nonlinear Hamiltonian systems

This paper aims to study a new reproducing kernel (RK) function-based collocation method for nonlinear Hamiltonian systems. By applying the associated functions of RK spaces W2,02, W2,03 and W2,04, we propose the second, third and fourth-order schemes, respectively. Since the coefficient matrix of t...

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Bibliographic Details
Published inApplied mathematics letters Vol. 136; p. 108451
Main Authors Niu, Jing, Jia, Yuntao, Sun, Jindong
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2023
Subjects
Collocation method
Energy conservation
Nonlinear Hamiltonian systems
RK function
Symplectic structure
Collocation method
Energy conservation
Nonlinear Hamiltonian systems
RK function
Symplectic structure
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ISSN0893-9659
1873-5452
DOI10.1016/j.aml.2022.108451

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Summary:This paper aims to study a new reproducing kernel (RK) function-based collocation method for nonlinear Hamiltonian systems. By applying the associated functions of RK spaces W2,02, W2,03 and W2,04, we propose the second, third and fourth-order schemes, respectively. Since the coefficient matrix of the linear system obtained by our scheme is symmetric and positive definite, our approach is uniquely solvable.The numerical experiments verify that our algorithms are efficient and can simulate the long time behavior including energy conservation and symplectic structure properties.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2022.108451