[PDF] Top 20 A high order finite difference scheme for a singularly perturbed reaction diffusion problem with an interior layer

... a high-order finite difference method for solving a singularly perturbed reaction-diffusion problem with a discontinuous source ...difference scheme is a combination of a ... See full document

... . Singularly perturbed differential equations arise many applications such as, fluid mechanics, chemical-reactor theory, the Navier-Stokes equations of fluid flow at high Reynolds number, control ... See full document

... of singularly perturbed boundary value problems for higher order nonlinear ordinary differential equations, which have important applications in Fluid Dynamics, can be found in [1,2,6- ...fourth ... See full document

... of singularly perturbed convection-diffusion equations is ...Il’in scheme on a uniform mesh. It is proved that the numerical scheme has first order accuracy, which is uniform ... See full document

... Singularly perturbed differential equations are typically characterized by a small parame- ter ε multiplying some or all of the highest order terms in the differential equations as nor- mally boundary ... See full document

... numerical scheme is proposed to examine the singularly perturbed time dependent differential- difference equation with turning point in one space dimen- sion on a rectangular ...considered ... See full document

... nonlinear singularly perturbed problems with nonlocal condition are evaluated by finite difference ...convergent finite difference scheme on Bakhvalov mesh is ...the ... See full document

... highest order derivative terms are said to be singularly perturbed and normally boundary layers occur in their ...boundary layer behavior of the ... See full document

... of singularly perturbed differential equations typ- ically exhibit sharp boundary and interior layers, which are narrow regions where solutions change ...of layer solu- tions in an efficient way, ... See full document

... of problem have also been considered 13, ...difference scheme on an equidistant mesh for the numerical solution of the linear three-point reaction-diffusion problem have been studied in ... See full document

... second order singularly perturbed problems (SPPs) in one- dimension, of reaction-convection-diffusion type, whose solution contains boundary layers; see, ...using finite ... See full document

... an interior subdomain, the narrow subdomain overlap being of width O(ε | lnh | ), where h is the maximum side length of mesh elements, and the global number of mesh nodes does not exceed O(h −2 ...on ... See full document

... solving singularly perturbed delay differential equations based on finite difference scheme, fitted mesh and B-spline method, piecewise uniform ...second order differential ... See full document

... difference scheme produces unstable solutions on both an equidistant mesh and an appropriate Shishkin mesh (compare these results with the solutions of the stabilised method that we propose in this paper, which are ... See full document

... the interior value of 4 just as quickly as for maximal interfacial subdomains, further iterations are required to smooth the oscillation in the boundary ... See full document

... The work contained in this paper falls under the second category. We use the nonstandard finite difference methods originally developed by Bakhvalov for some other problems. One of the simplest ways to derive such ... See full document

... a scheme based on cubic spline in compression which com- prises an exponentially fitted difference scheme on a uniform ...difference scheme based on cubic spline in compression for a second order ... See full document

... leading order since higher order terms of the inner layer solution depend on the actual value of ...inner layer solution decays to zero as the stretched variable approaches infinity, like the ... See full document

... [4] Feng, Z.S. (2003) Traveling Solitary Wave Solutions to the Generalized Boussinesq Equation. Wave Motion , 37, 17-23. https://doi.org/10.1016/S0165-2125(02)00019-7 [5] Song, C., Li, H. and Li, J. (2013) Initial ... See full document

... delay differential equations have attracted the attention of many sciences and engineers. The Chebyshev expan- sion methods are used to solve the singularly-perturbed delay differential equations ... See full document