Pointwise error estimates for a system of two singularly perturbed time‐dependent semilinear reaction–diffusion equations

2021 ◽  
Author(s):  
S. Chandra Sekhara Rao ◽  
Abhay Kumar Chaturvedi
Keyword(s):  
Error Estimates ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Singularly Perturbed ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Pointwise Error ◽  
Pointwise Error Estimates

Pointwise Error Estimates for the LDG Method Applied to 1-d Singularly Perturbed Reaction-Diffusion Problems

2013 ◽  
Vol 13 (1) ◽  
pp. 79-94 ◽  
Author(s):  
Huiqing Zhu ◽  
Zhimin Zhang
Keyword(s):  
Error Estimates ◽  
Reaction Diffusion ◽  
Local Discontinuous Galerkin Method ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
One Dimensional ◽  
Pointwise Error ◽  
Ldg Method ◽  
Pointwise Error Estimates ◽  
Diffusion Problems

Abstract. The local discontinuous Galerkin method (LDG) is considered for solving one-dimensional singularly perturbed two-point boundary value problems of reaction-diffusion type. Pointwise error estimates for the LDG approximation to the solution and its derivative are established on a Shishkin-type mesh. Numerical experiments are presented. Moreover, a superconvergence of order of the numerical traces is observed numerically.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Sign in / Sign up

Export Citation Format

Share Document