Higher order accurate approximations on equidistributed meshes for boundary layer originated mixed type reaction diffusion systems with multiple scale nature
By Pratibhamoy Das, Subrata Rana, Jesús Vigo-Aguiar. 2020
112 citations recorded by the source corpus.
Abstract In the present research, we consider a boundary layer originated system of reaction diffusion problems whose boundary conditions are of mixed type. This problem is singularly perturbed nature and the diffusion parameters are considered to be of different magnitude. We develop two adaptive methods based on r-refinement strategy, which move the mesh points toward the boundary layers. Here, we use a curvature based monitor function for adaptive moving mesh generation. Based on a combination of forward and backward difference schemes on this adaptively generated equidistributed mesh, we obtain a first order uniformly accurate solution. The discrete solution can be enhanced to a second order uniform accuracy by our proposed cubic spline based scheme. Numerically, we provide a comparison of our present method on the proposed adaptive moving meshes with the commonly used meshes. Experiments show the highly effective behavior of the present method.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/ffd0511271e126aad38a2656c58aaf19655ab265
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
In Computational Theory and Mathematics
In Numerical Analysis
Citations in the corpus
- Theoretical prospects of fractional order weakly singular Volterra Integro differential equations and their approximations with convergence analysis (2021, methodology): “Using (25), the initial condition and equating the coefficient of O(pj), we obtain the following outcome O(p0) ∶ L(W0(x)) − f (x) = 0 ⇒ W0(x) = x + x7∕2 + √ πx9∕4 10Γ(13∕4) + 7 √ πx13∕4 26Γ(13∕4) + 2πx 19∕4 627Γ(9∕4) + 105πx 23∕4 876Γ(15∕4) .”