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| 001 | 860700 | ||
| 005 | 20210130000602.0 | ||
| 024 | 7 | _ | |a 10.1016/j.cam.2019.01.040 |2 doi |
| 024 | 7 | _ | |a 0377-0427 |2 ISSN |
| 024 | 7 | _ | |a 1879-1778 |2 ISSN |
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| 037 | _ | _ | |a FZJ-2019-01365 |
| 041 | _ | _ | |a English |
| 082 | _ | _ | |a 510 |
| 100 | 1 | _ | |a Martín-Vaquero, J. |0 0000-0001-5118-5576 |b 0 |e Corresponding author |
| 245 | _ | _ | |a ESERK5: A fifth-order extrapolated stabilized explicit Runge–Kutta method |
| 260 | _ | _ | |a Amsterdam |c 2019 |b North-Holland |
| 336 | 7 | _ | |a article |2 DRIVER |
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| 520 | _ | _ | |a A new algorithm is developed and analyzed for multi-dimensional non-linear parabolic partial differential equations (PDEs) which are semi-discretized in the spatial variables leading to a system of ordinary differential equations (ODEs). It is based on fifth-order extrapolated stabilized explicit Runge–Kutta schemes (ESERK). They are explicit methods, and therefore it is not necessary to employ complicated software for linear or non-linear system of equations. Additionally, they have extended stability regions along the negative real semi-axis, hence they can be considered to solve stiff problems coming from very common diffusion or reaction–diffusion problems.Previously, only lower-order codes (up to fourth-order) have been constructed and made available in the scientific literature. However, at the same time, higher-order codes were demonstrated to be very efficient to solve equations where it is necessary to have a high precision or they have transient zones that are very severe, and where functions change very fast. The new schemes allow changing the step length very easily and with a very small computational cost. Thus, a variable step length, with variable number of stages algorithm is constructed and compared with good numerical results in relation to other well-known ODE solvers. |
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| 700 | 1 | _ | |a Kleefeld, Andreas |0 P:(DE-Juel1)169421 |b 1 |u fzj |
| 773 | _ | _ | |a 10.1016/j.cam.2019.01.040 |g p. S0377042719300561 |0 PERI:(DE-600)1468806-2 |p 22-36 |t Journal of computational and applied mathematics |v 356 |y 2019 |x 0377-0427 |
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