A note on numerically consistent initial values for high index differential-algebraic equations
When differential-algebraic equations of index 3 or higher are solved with backward differentiation formulas, the solution can have gross errors in the first few steps, even if the initial values are equal to the exact solution and even if the stepsize is kept constant. This raises the question of w...
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| Published in | Electronic transactions on numerical analysis Vol. 34; p. 14 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Institute of Computational Mathematics
01.12.2008
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1068-9613 1097-4067 1097-4067 |
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| Abstract | When differential-algebraic equations of index 3 or higher are solved with backward differentiation formulas, the solution can have gross errors in the first few steps, even if the initial values are equal to the exact solution and even if the stepsize is kept constant. This raises the question of what are consistent initial values for the difference equations. Here we study how to change the exact initial values into what we call numerically consistent initial values for the implicit Euler method. Key words. high index differential-algebraic equations, consistent initial values AMS subject classifications. 65L05 |
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| AbstractList | When differential-algebraic equations of index 3 or higher are solved with backward differentiation formulas, the solution in the first few steps can have gross errors, the solution can have gross errors in the first few steps, even if the initial values are equal to the exact solution and even if the step size is kept constant. This raises the question of what are consistent initial values for the difference equations. Here we study how to change the exact initial values into what we call numerically consistent initial values for the implicit Euler method. When differential-algebraic equations of index 3 or higher are solved with backward differentiation formulas, the solution can have gross errors in the first few steps, even if the initial values are equal to the exact solution and even if the stepsize is kept constant. This raises the question of what are consistent initial values for the difference equations. Here we study how to change the exact initial values into what we call numerically consistent initial values for the implicit Euler method. Key words. high index differential-algebraic equations, consistent initial values AMS subject classifications. 65L05 When differential-algebraic equations of index 3 or higher are solved with backward differentiation formulas, the solution can have gross errors in the first few steps, even if the initial values are equal to the exact solution and even if the stepsize is kept constant. This raises the question of what are consistent initial values for the difference equations. Here we study how to change the exact initial values into what we call numerically consistent initial values for the implicit Euler method. |
| Audience | Academic |
| Author | Arevalo, Carmen |
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| SubjectTerms | Differential equations Matematik Mathematical Sciences Natural Sciences Naturvetenskap Numerical analysis |
| Title | A note on numerically consistent initial values for high index differential-algebraic equations |
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