scholarly journals Numerical Solution of MRLW Equation with İmplicit Finite-Difference Approximation

2019 ◽  
Keyword(s):  
Finite Difference ◽  
Numerical Solution ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Implicit Finite Difference

scholarly journals NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS IN IRREGULAR PLANE REGIONS USING QUALITY STRUCTURED CONVEX GRIDS

2013 ◽  
Vol 04 (02) ◽  
pp. 1350004
Author(s):  
F. DOMÍNGUEZ-MOTA ◽  
P. FERNÁNDEZ-VALDEZ ◽  
S. MENDOZA-ARMENTA ◽  
G. TINOCO-GUERRERO ◽  
J. G. TINOCO-RUIZ
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Numerical Solution ◽  
Poisson Equation ◽  
Finite Differences ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Structured Grids ◽  
Simply Connected ◽  
Simply Connected Domains

The variational grid generation method is a powerful tool for generating structured convex grids on irregular simply connected domains whose boundary is a polygonal Jordan curve. Several examples that show the accuracy of a finite difference approximation to the solution of a Poisson equation using this kind of structured grids have been recently reported. In this paper, we compare the accuracy of the numerical solution calculated using those structured grids and finite differences against the solution obtained with Delaunay-like triangulations on irregular regions.

scholarly journals On the numerical solutions for a parabolic system with blow-up

2021 ◽  
Vol 6 (11) ◽  
pp. 11749-11777
Author(s):  
Chien-Hong Cho ◽  
◽  
Ying-Jung Lu ◽  
Keyword(s):  
Exact Solution ◽  
Finite Difference ◽  
Numerical Solution ◽  
Parabolic System ◽  
Numerical Solutions ◽  
Blow Up ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Blow Up Rate ◽  
Axisymmetric Solutions

<abstract><p>We study the finite difference approximation for axisymmetric solutions of a parabolic system with blow-up. A scheme with adaptive temporal increments is commonly used to compute an approximate blow-up time. There are, however, some limitations to reproduce the blow-up behaviors for such schemes. We thus use an algorithm, in which uniform temporal grids are used, for the computation of the blow-up time and blow-up behaviors. In addition to the convergence of the numerical blow-up time, we also study various blow-up behaviors numerically, including the blow-up set, blow-up rate and blow-up in $ L^\sigma $-norm. Moreover, the relation between blow-up of the exact solution and that of the numerical solution is also analyzed and discussed.</p></abstract>

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