Examples of transformations improving the numerical accuracy of the integration of differential equations

Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations - Lecture Notes in Mathematics ◽

10.1007/bfb0066593 ◽

1974 ◽

pp. 207-236 ◽

Cited By ~ 13

Author(s):

J. Baumgarte ◽

E. Stiefel

Keyword(s):

Differential Equations ◽

Numerical Accuracy

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Numerical Accuracy of the Predictor-Corrector Method to Solve Fuzzy Differential Equations Based on the Stochastic Arithmetic

Fuzzy Information and Engineering ◽

10.1080/16168658.2021.1880134 ◽

2021 ◽

pp. 1-20

Author(s):

Mohammad Ali Fariborzi Araghi ◽

Hasan Barzegar Kelishami

Keyword(s):

Differential Equations ◽

Numerical Accuracy ◽

Stochastic Arithmetic ◽

Predictor Corrector

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Linear Visco-Resistive Computations of Magnetohydrodynamic Waves: I. The Code and Test Cases

International Astronomical Union Colloquium ◽

10.1017/s0252921100025926 ◽

1994 ◽

Vol 144 ◽

pp. 503-505

Author(s):

R. Erdélyi ◽

M. Goossens ◽

S. Poedts

Keyword(s):

Resonant Absorption ◽

Numerical Code ◽

Mhd Waves ◽

Test Cases ◽

Numerical Accuracy ◽

Element Discretization ◽

Flux Tubes ◽

Magnetohydrodynamic Waves ◽

Viscosity Coefficients ◽

Magnetic Flux Tubes

AbstractThe stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. Our computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code.

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