Orthogonal cubic spline collocation method for the Cahn–Hilliard equation

A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn–Hilliard equation

“…Ye [40] has also used the Legendre collocation method to study this problem with Neumann boundary conditions. Danumjaya and Nandakumaran [41] have employed the orthogonal cubic spline collocation method for this equation. He et al [38] have analyzed a class of large time-stepping methods for this equation.…”

“…There have been many algorithms developed and simulations performed for the C-H equations, using Finite Element Methods [18][19][20][21][22][23][24][25], Discontinuous Galerkin Techniques [26][27][28], Finite Difference Schemes [29][30][31][32][33][34][35][36], Spectral Methods [37,38], Collocation Techniques [39][40][41], Adomian Decomposition Procedure [42], m-transform [43] and etc.…”

The least squares spectral element method for the Cahn–Hilliard equation

“…Different numerical schemes to solve the C-H equation have been suggested in the literature. Among these are finite element approaches [16][17][18][19], finite difference schemes [20,21], discontinuous Galerkin techniques [22][23][24], Fourier spectral methods [25,26], collocation techniques [27], lattice Boltzmann method [28,6], boundary element method [29], multigrid techniques [30], among others. In addition, some adaptive grid techniques have also been presented [31,32].…”

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

“…Related to fourth-order evolution equations, in Pani and Chung [18], a C 1 -conforming finite element method is analyzed for the Rosenau equation. Numerical studies of one-dimensional and multidimensional Cahn-Hilliard equation are discussed by Elliott et al [19], [20], Danumjaya et al [21], and Qiang and Nicolaides [22]. Existence and numerical approximations of periodic solutions of semilinear fourth-order differential equations related to either extended Fisher-Kolmogorov equation or Swift-Hohenberg equation are discussed in Julia Chaparova [23].…”