Journal ArticleDOI
A moving mesh refinement based optimal accurate uniformly convergent computational method for a parabolic system of boundary layer originated reaction–diffusion problems with arbitrary small diffusion terms
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In this article, an optimal order uniformly accurate boundary layer adaptive method moving mesh method is proposed, which is able to capture the layer phenomena without using a priori information of the solution.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2020-08-27. It has received 40 citations till now. The article focuses on the topics: Discretization & Backward Euler method.read more
Citations
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A graded mesh refinement approach for boundary layer originated singularly perturbed time-delayed parabolic convection diffusion problems
TL;DR: An adaptive graded mesh generation algorithm, which is based on an entropy function in conjunction with the classical difference schemes, to resolve the layer behavior and several examples are presented to show the high performance of the proposed algorithm.
Journal ArticleDOI
Theoretical prospects of fractional order weakly singular Volterra Integro differential equations and their approximations with convergence analysis
Pratibhamoy Das,Subrata Rana +1 more
Journal ArticleDOI
Robust numerical method for singularly perturbed semilinear parabolic differential difference equations
TL;DR: In this article, the robust numerical method for solving the singularly perturbed semilinear partial differential equation with the spatial delay is presented, which is shown to be first-order convergent.
Journal ArticleDOI
Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations
TL;DR: In this article, two different methods to solve a time fractional partial integro-differential equation were proposed, i.e., Adomian decomposition method and homotopy perturbation method.
Journal ArticleDOI
Fitted mesh method for singularly perturbed parabolic problems with an interior layer
TL;DR: In this paper, the fitted mesh numerical method is presented to solve parabolic problems involving an interior layer, where a uniform mesh was applied in the temporal direction and fitted mesh type on the space variable yields the discrete problem.
References
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Journal ArticleDOI
Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]
Book
Robust Computational Techniques for Boundary Layers
TL;DR: In this paper, numerical methods for problems with Boundary Layers are presented. But they do not address the problems with Frictionless Walls and No Slip Boundary Conditions, and they are not suitable for Non-Monotone Methods in two dimensions.
Journal ArticleDOI
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
TL;DR: This paper considers several moving mesh partial differential equations that are related to the equidistribution principle, several of which are new, and some correspond to discrete moving mesh equations that have been used by others.
Book
Adaptive Moving Mesh Methods
Weizhang Huang,Robert D. Russell +1 more
TL;DR: This paper presents a meta-analyses of PDEs on Time-Varying Meshes and their effects on Mesh Adaption and Velocity-Based Adaptive Methods, and some of the methods used to develop these methods are described.
Book
Singular Perturbation Methodology in Control Systems
TL;DR: In this paper, the twin topics of singular perturbation methods and time scale analysis to problems in systems and control are discussed, and the heart of the book is the singularly perturbed optimal control systems which are notorious for demanding excessive computational costs.