Table 2 Comparison of the numerical solutions obtained with various values of m for \(N = 10 , T = 1\), and \(\tau =0.5\) with the exact solution for example 2
From: Linear B-spline finite element method for the generalized diffusion equation with delay
x | Numerical solutions | Exact solution | |||
|---|---|---|---|---|---|
m =10 | m =20 | m =40 | m =80 | Â | |
0.1\(\pi\) | 0.187408 | 0.187423 | 0.187427 | 0.187427 | 0.187428 |
0.2\(\pi\) | 0.356472 | 0.356500 | 0.356507 | 0.356509 | 0.356509 |
0.3\(\pi\) | 0.490642 | 0.490680 | 0.490690 | 0.490692 | 0.490693 |
0.4\(\pi\) | 0.576784 | 0.576829 | 0.576841 | 0.576843 | 0.576844 |
0.5\(\pi\) | 0.606467 | 0.606514 | 0.606526 | 0.606529 | 0.606530 |
0.6\(\pi\) | 0.576784 | 0.576829 | 0.576841 | 0.576843 | 0.576844 |
0.7\(\pi\) | 0.490642 | 0.490680 | 0.490690 | 0.490692 | 0.490693 |
0.8\(\pi\) | 0.356472 | 0.356500 | 0.356507 | 0.356509 | 0.356509 |
0.9\(\pi\) | 0.187408 | 0.187423 | 0.187427 | 0.187427 | 0.187428 |