| 30 | | For the implementation it is advantageous to compute ψ^N^ from the intermediate solutions ψ^1^ and ψ^2^ as follows: |
| | 30 | For the implementation it is advantageous to compute ψ^N^ from the intermediate solutions ψ^1^ and ψ^2^ and combine the local tendencies in one array to save storage (therefor low-storage scheme) as follows: |
| | 31 | {{{ |
| | 32 | #!Latex |
| | 33 | \[ \hat\psi_{1} & = & \psi_{n} + \frac{1}{3} \Delta t f\left(\psi_{n}\right) \] |
| | 34 | \[ \hat\psi_{2} & = & \hat\psi_{1} + \frac{1}{48} \Delta t \left( 45 f\left(\hat\psi_1\right) - 25 f\left(\psi_{n}\right) \] |
| | 35 | f\left(\hat\psi_{1}\right) & = &-153 f\left(\hat\psi_{1}\right) + 85 f\left(\psi_{n}\right) \] |
| | 36 | \[ \hat\psi_{3} & = & \left( \psi_{n+1} \right) = \hat\psi_{2} + \frac{1}{240} \Delta t \left( 128 f\left(\hat\psi_2\right) + 16 \left(\hat\psi_{1}\right) \] |
| | 37 | }}} |
