Sentence examples for moving collocation methods from inspiring English sources

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

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

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.

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

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.

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

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.

The fully discrete moving collocation method proposed is shown to be fourth-order convergent in space and it is then employed to simulate the blow-up solutions to the generalized KdV equations.