An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations

Liu, Changying; Shi, Wei; Wu, Xinyuan

doi:10.1016/j.amc.2014.08.077

Cited by 10 publications

(22 citation statements)

References 26 publications

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“…In , for solving the similar oscillatory system (20), an

s

‐stage ERKN integrator with step size

τ

(see scheme [41]) is used. In this article, we use the same scheme in to solve the oscillatory system (20). The difference between our article and is matrix

M

.…”

Section: Pdes To Odes By Fourth Order Compact Discretizations Of Spatmentioning

confidence: 99%

“…In this article, we use the same scheme in to solve the oscillatory system (20). The difference between our article and is matrix

M

.…”

Section: Pdes To Odes By Fourth Order Compact Discretizations Of Spatmentioning

confidence: 99%

“…(see, )

| f (u_{1}) - f (u_{2}) | \leq L | u_{1} - u_{2} | \forall u_{1}, u_{2} .

The main property of the Eq. (1) is the conservation of energy given by (see, )

E = E (t) = \frac{1}{2} \int_{x_{l}}^{x_{r}} (u_{t}^{2} + a^{2} u_{x}^{2} + 2 G (u)) d x .

…”

Section: Introductionmentioning

confidence: 98%

“…Bratsos , proposed a apredictor‐corrector scheme based on second‐order approximants of the matrix exponential term in a three‐time level reccurence relation. In , the authors considered a novel high order explicit scheme, applying a fourth‐order finite difference scheme in space and a multidimensional extended Runge‐Kutta‐Nystrom (ERKN) method in time integration.…”

Section: Introductionmentioning

confidence: 99%

“…(1). The proposed method is based on a compact approximation of fourth order by the integral method with variational limit in space and the same method in in temporal components.…”

Section: Introductionmentioning

confidence: 99%

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Fourth‐order compact and energy conservative scheme for solving nonlinear Klein‐Gordon equation

Luo

Guo

2017

Numerical Methods Partial

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In this article, a fourth-order compact and conservative scheme is proposed for solving the nonlinear Klein-Gordon equation. The equation is discretized using the integral method with variational limit in space and the multidimensional extended Runge-Kutta-Nyström (ERKN) method in time. The conservation law of the space semidiscrete energy is proved. The proposed scheme is stable in the discrete maximum norm with respect to the initial value. The optimal convergent rate is obtained at the order of O(h 4 ) in the discrete L ∞ -norm. Numerical results show that the integral method with variational limit gives an efficient fourthorder compact scheme and has smaller L ∞ error, higher convergence order and better energy conservation for solving the nonlinear Klein-Gordon equation compared with other methods under the same condition.

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“…In , for solving the similar oscillatory system (20), an

s

‐stage ERKN integrator with step size

τ

(see scheme [41]) is used. In this article, we use the same scheme in to solve the oscillatory system (20). The difference between our article and is matrix

M

.…”

Section: Pdes To Odes By Fourth Order Compact Discretizations Of Spatmentioning

confidence: 99%

“…In this article, we use the same scheme in to solve the oscillatory system (20). The difference between our article and is matrix

M

.…”

Section: Pdes To Odes By Fourth Order Compact Discretizations Of Spatmentioning

confidence: 99%

“…(see, )

| f (u_{1}) - f (u_{2}) | \leq L | u_{1} - u_{2} | \forall u_{1}, u_{2} .

The main property of the Eq. (1) is the conservation of energy given by (see, )

E = E (t) = \frac{1}{2} \int_{x_{l}}^{x_{r}} (u_{t}^{2} + a^{2} u_{x}^{2} + 2 G (u)) d x .

…”

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

“…(1). The proposed method is based on a compact approximation of fourth order by the integral method with variational limit in space and the same method in in temporal components.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations