1 Introduction
2 The Wave Equation on Second Order Form
2.1 An Error Bound for the Continuous Problem
3 The Semi-discrete Wave Equation on Second Order Form
3.1 An Error Bound for the Semi-discrete Problem
3.2 The Fully Discrete Numerical Scheme
4 Numerical Results
N | SBP(2,1) | Rate | SBP(4,2) | Rate | SBP(6,3) | Rate |
---|---|---|---|---|---|---|
10 |
\(4.1\times 10^{-2}\)
| − |
\(8.6\times 10^{-2}\)
| − |
\(7.2\times 10^{-2}\)
| − |
20 |
\(1.1\times 10^{-2}\)
| 1.9 |
\(1.1\times 10^{-2}\)
| 3.0 |
\(2.2\times 10^{-3}\)
| 5.0 |
40 |
\(2.9\times 10^{-3}\)
| 1.9 |
\(1.2\times 10^{-3}\)
| 3.2 |
\(1.6\times 10^{-4}\)
| 3.8 |
80 |
\(7.3\times 10^{-4}\)
| 1.9 |
\(1.4\times 10^{-4}\)
| 3.1 |
\(9.8\times 10^{-6}\)
| 4.0 |
160 |
\(2.9\times 10^{-4}\)
| 2.0 |
\(1.6\times 10^{-5}\)
| 3.1 |
\(5.4\times 10^{-7}\)
| 4.2 |