A finite difference method for a numerical solution of elliptic boundary value problems
and
Oct 03, 2018
About this article
Published Online: Oct 03, 2018
Page range: 311 - 320
Received: Mar 18, 2018
Accepted: Jun 26, 2018
DOI: https://doi.org/10.21042/AMNS.2018.1.00024
Keywords
© 2018 P.K. Pandey and S.S.A. Jaboob, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
Fig. 1
Maximum absolute errors in u(x, y) in Ω1 and Ω2 for problem 1_
| MAU | |||
|---|---|---|---|
| N | Ω1 | Ω2 | Etime |
| 4 | .44357300(-1) | .10435032(-1) | 0.0 |
| 8 | .20332336(-1) | .76701991(-1) | 0.0 |
| 16 | .14885783(-1) | .68618409(-1) | 0.1 |
| 32 | .14406562(-1) | .66433303(-1) | 0.9 |
| 64 | .14742970(-1) | .65848224(-1) | 10.9 |
| 128 | .15002966(-1) | .65623157(-1) | 134.9 |
a0=0_516,a1=1_0−a02_0,$\begin{array}{} a_0=\frac{0_5}{16}, a_1=1_0-\frac{a_0}{2_0}, \end{array}$a2 = a0 exp(–1:5)
| MAU | |||
|---|---|---|---|
| N | Ω1 | Ω2 | Etime |
| 4 | .27722120(-2) | .65218653(-2) | 0.0 |
| 8 | .12705326(-2) | .47935690(-2) | 0.0 |
| 16 | .92923641(-3) | .42875255(-2) | 0.1 |
| 32 | .89609623(-3) | .41472162(-2) | 0.7 |
| 64 | .90408325(-3) | .40954794(-2) | 7.1 |
| 128 | .84555149(-3) | .39971317(-2) | 62.1 |
a0=0_5128,a1=1_0−a02_0,$\begin{array}{} a_0=\frac{0_5}{128}, a_1=1_0-\frac{a_0}{2_0}, \end{array}$a2 = a0 exp(–1:5)
| MAU | |||
|---|---|---|---|
| N | Ω1 | Ω2 | Etime |
| 4 | .34630299(-3) | .81500964(-3) | 0.0 |
| 8 | .15854836(-3) | .59888320(-3) | 0.0 |
| 16 | .11491776(-3) | .53451018(-3) | 0.1 |
| 32 | .10740757(-3) | .51317172(-3) | 0.4 |
| 64 | .89645386(-4) | .48682650(-3) | 3.4 |
| 128 | .48041344(-4) | .44426878(-3) | 15.4 |