Stability and convergence of compact finite difference method for parabolic problems with delay

A new compact alternating direction implicit method for solving two dimensional time fractional diffusion equation with Caputo-Fabrizio derivative

“…Low-order finite difference schemes are not accurate enough for solving many problems in science. Recently the focus has shifted to high order compact finite difference methods [20][21][22][23]. The advantage of the high order compact finite difference is that they give high accuracy on small stencils with greater computational efficiency [24].…”

Compact Finite Differences Method for FitzHugh-Nagumo Equation

“…Mohanty et al [14] used new two-level implicit compact operator method for the solution of Burgers-Huxley equation. In a study, the authors of a paper [5] derived solution of the parabolic problems with delay using compact finite difference methods. Wang et al [17] applied compact finite difference scheme to study the coupled Gross-Pitaevskii equations.…”

Linear θ-Method and Compact θ-Method for Generalised Reaction-Diffusion Equation with Delay

“…By the same technique used in [22], one can check that | | < 1. Next, to verify the rest of items of Lemma 6, that is,…”

“…Taking the analytical technique in [20][21][22], we know that the linear -method (8) is asymptotically stable about the trivial solution if and only if…”

“…In this study, we use the following model as the test equation for analysing stability of the numerical method, which is an extension to the previous work [20][21][22]. The standard second-order central difference method and compact finite difference method are utilised to discrete the diffusion operator, respectively, and the linear -method is utilised to discrete the temporal direction.…”