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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Vydáno v:Applied mathematics letters Ročník 136; s. 108451
Hlavní autoři: Niu, Jing, Jia, Yuntao, Sun, Jindong
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.02.2023
Témata:
Collocation method
Energy conservation
Nonlinear Hamiltonian systems
RK function
Symplectic structure
Collocation method
Energy conservation
Nonlinear Hamiltonian systems
RK function
Symplectic structure
ISSN:0893-9659, 1873-5452
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Shrnutí: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