Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods

Improved upwind discretization of the advection equation

“…Only a glimpse of EF methods for time dependent PDEs is given through the article. Recently, EF methods are proven to be very successful in time integration of wave equations in . However, employing EF methods in both space and time integration has not been investigated in the literature.…”

Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations

“…Wu et al [37,20]. If the coefficients of an s-stage ERKN method satisfy the following conditions respectively.…”

“…It is known that most of integrators adapted to the oscillatory problems are frequency-dependent, such as ARKN methods [13][14][15][16][17], ERKN methods [18][19][20][21], and trigonometrically/exponentially-fitted methods [22][23][24][25]. For nonlinear Schrödinger equations, taking the frequency of the problem into account, several useful trigonometrically/exponentially-fitted methods are proposed (see, e.g., [26][27][28][29][30][31][32]).…”

Triangular splitting implementation of RKN‐type Fourier collocation methods for second‐order differential equations

“…Such problems often arise in many fields of applied sciences such as applied mathematics, celestial mechanics, physics, quantum chemistry, and electronics. Many effective numerical methods have been developed and studied for solving the second-order system (1) such as Runge-Kutta-Nyström (RKN) methods and multistep methods (see, eg, previous studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] ). It is well known that an s-stage fully implicit RKN method involves an sd-dimensional nonlinear system.…”