Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation

A fourth‐order H1‐Galerkin mixed finite element method for Kuramoto–Sivashinsky equation

“…Further, a similar finding on chaotic behavior of the numerical solution of Kuramoto-Sivashinsky equation can be seen in Ref. [7].…”

“…The advantage of this method for both semi-discrete and fully discrete cases is that the size of each resulting linear system (i.e., (n + 1) × (n + 1)) is near to half of the size (i.e., (2n + 1) × (2n + 1)) of the matrix as in the method described in Ref. [7]. This is clearly explained in section 6 in which linear fully discrete scheme is described.…”

“…In Ref. [7], a second-order splitting combined with orthogonal cubic spline collocation method is considered for the same problem. There are some advantages of this method over that presented in Ref.…”

“…[6], Collet et al studied the analyticity properties of solutions of the Kuramoto-Sivashinsky equation having periodic initial condition with period L, and numerical experiments are presented showing the region of analyticity. The kind of boundary conditions in (1.2) is considered by authors of research articles [7], [8], and [9]. Further, these boundary conditions are referred as "physical Dirichlet-like boundary conditions" in Ref.…”

“…In Ref. [7] Manikkam et al, a second-order splitting combined with orthogonal cubic spline collocation method for (1.1) is formulated, analyzed, and the error bounds are obtained for the semi-discrete scheme.…”