Restrictive Taylor's approximation for solving convection–diffusion equation

A fourth-order method of the convection–diffusion equations with Neumann boundary conditions

“…Similarly we can prove Eq. (11). Assume that u(x, t) is the exact solution of problem (1), then, according to Theorem 1, we have…”

“…With the rapid progress in computer power, the differential convection-diffusion equations can be analytically studied by pursuing the numerical solution of their discretized counterparts. Many numerical methods have been developed to solve the convection-diffusion equations with Dirichlet boundary conditions, see [1][2][3][4][5][6][7][8][9][10][11][12][13].…”

Analytical and approximate solution of two-dimensional convection-diffusion problems

“…And some numerical solutions have been developed to solve these types of convection-diffusion problems. likes: Higher-Order ADI method [10] or rational high-order compact ADI method [11], the alternating direction implicit method [12], the finite element method [13], fourth-order compact finite difference method [14], decomposition Method [15], the finite difference method [16], restrictive taylors approximation [17], The fundamental solution [18], finite difference method [19], combined compact difference scheme and alternating direction implicit method [20], higher order compact schemes method [21], the finite volume method [22], the finite difference and legendre spectral method [23] and even the Monte *Corresponding Author Carlo method [24]. Keskin in [25] proposed the RDTM to solve various PDE and fractional nonlinear partial differential equations.…”

Analytical Solutions of One-Dimensional Convection-Diffusion Problems

“…In recent years, some numerical solution have been developed to solve these types of convection-diffusion problems. Likes: the adaptive spline function approximation [1], several finite element methods [2], the finite difference approximation [3], cubic B-spline quasi-interpolation [4], restrictive taylor's approximation [5], exponential B-spline collocation method [6]. Exponential B-splines [7], weighted finite difference [8], meshless method [9], implicit method [10], redefined cubic B-splines collocation method [11].…”