Sentence examples for moving collocation scheme from inspiring English sources

For the KdV equations which are nonlinear, it is indeed not guaranteed that the moving collocation scheme can attain the sixth-order convergence.

The moving collocation method is carried out by solving the coupled system consisting of an MMPDE and {(12), (13)}.

In this paper, we develop the moving collocation method for third-order PDEs - the KdV equations.

The convergence analysis of the moving collocation methods was given by Ma et al. [12].

We shall vary the number of mesh subintervals N to test the order of convergence of our moving collocation method.

In this section, we demonstrate the efficiency and accuracy of the proposed moving collocation method for solving GKdV equations.

Later moving collocation methods were developed to solve fourth-order PDEs [10] and fractional-order PDEs [11].

The conservative moving collocation method, which is introduced by Huang and Russell [14], will be used to discretize the main equation.

(9) Based on the moving mesh (x xi,t)), a conservative moving collocation method with quintic Hermite spline basis is employed to discretize the GKdV equation (1).

The conservative moving collocation method with cubic Hermite spline basis was proposed by Huang and Russell in [9] to solve second-order time-dependent PDEs.

Applied to second- and fourth-order PDEs [9, 10], moving collocation methods show a high order of convergence and capabilities of capturing blow-up phenomena.